3. ELEMENTS OF QUANTUM MECHANICS

3.1.Wave function

Every microparticle is a special kind of formation, combining the properties of both particles and waves. The difference between a microparticle and a wave is that it is detected as an indivisible whole. For example, no one has observed a half-electron. At the same time, the wave can be divided into parts and then each part can be perceived separately.

The difference between a microparticle in quantum mechanics and an ordinary microparticle is that it does not simultaneously have certain values ​​of coordinates and momentum, so the concept of a trajectory for a microparticle loses its meaning.

The probability distribution of finding a particle at a given time in a certain region of space will be described by the wave function (x, y, z , t) (psi function). Probability dP that the particle is located in a volume element dV, proportional
and volume element dV:

dP=
dV.

Physical meaning has not the function itself
, and the square of its modulus is the probability density. It determines the probability of a particle being at a given point in space.

Wave function
is the main characteristic of the state of microobjects (microparticles). With its help, in quantum mechanics, the average values ​​of physical quantities that characterize a given object in a state described by the wave function can be calculated
.

3.2. Uncertainty principle

In classical mechanics, the state of a particle is specified by coordinates, momentum, energy, etc. These are dynamic variables. A microparticle cannot be described by such dynamic variables. The peculiarity of microparticles is that not all variables are obtained in measurements. certain values. For example, a particle cannot have both exact values coordinates X and impulse components R X. Uncertainty of values X And R X satisfies the relation:

(3.1)

– the smaller the uncertainty of the coordinate Δ X, the greater the uncertainty of the pulse Δ R X, and vice versa.

Relation (3.1) is called the Heisenberg uncertainty relation and was obtained in 1927.

Δ values X and Δ R X are called canonically conjugate. The same canonically conjugate are Δ at and Δ R at, and so on.

The Heisenberg Uncertainty Principle states that the product of the uncertainties of two conjugate variables cannot be less than Planck's constant in order of magnitude. ħ.

Energy and time are also canonically conjugate, therefore
. This means that the determination of energy with an accuracy of Δ E should take time interval:

Δ t ~ ħ/ Δ E.

Let's determine the coordinate value X freely flying microparticle, placing in its path a gap of width Δ X, located perpendicular to the direction of particle motion. Before the particle passes through the slit, its momentum component is R X has the exact meaning R X= 0 (the gap is perpendicular to the momentum vector), so the uncertainty of the momentum is zero, Δ R X= 0, but the coordinate X particles is completely uncertain (Fig. 3.1).

IN the moment the particle passes through the slit, the position changes. Instead of complete uncertainty of coordinates X uncertainty appears Δ X, and momentum uncertainty Δ appears R X .

Indeed, due to diffraction, there is some probability that the particle will move within an angle of 2 φ , Where φ – the angle corresponding to the first diffraction minimum (we neglect the maxima of higher orders, since their intensity is small compared to the intensity of the central maximum).

Thus, uncertainty arises:

Δ R X =R sin φ ,

But sin φ = λ / Δ X– this is the condition of the first minimum. Then

Δ R X ~рλ/Δ X,

Δ XΔ R X ~рλ= 2πħ ≥ħ/ 2.

The uncertainty relationship indicates to what extent the concepts of classical mechanics can be used in relation to microparticles, in particular, with what degree of accuracy can we talk about the trajectory of microparticles.

Movement along a trajectory is characterized by certain values ​​of the particle’s speed and its coordinates at each moment of time. Substituting into the uncertainty relation instead R X expression for momentum
, we have:

–

The greater the mass of the particle, the less uncertainty in its coordinates and speed, the more accurately the concepts of trajectory are applicable to it.

For example, for a microparticle with a size of 1·10 -6 m, the uncertainties Δх and Δ go beyond the accuracy of measuring these quantities, and the movement of the particle is inseparable from the movement along the trajectory.

The uncertainty relation is a fundamental proposition of quantum mechanics. For example, it helps explain the fact that an electron does not fall on the nucleus of an atom. If an electron fell on a point nucleus, its coordinates and momentum would take on certain (zero) values, which is incompatible with the uncertainty principle. This principle requires that the uncertainty of the electron coordinate Δ r and momentum uncertainty Δ R satisfied the relation

Δ rΔ p ≥ ħ/ 2,

and meaning r= 0 is impossible.

The energy of an electron in an atom will be minimal at r= 0 and R= 0, so to estimate the lowest possible energy we set Δ r ≈ r, Δ p ≈ p. Then Δ rΔ p ≥ ħ/ 2, and for lowest value we have uncertainties:

we are only interested in the order of magnitudes included in this relation, so the factor can be discarded. In this case we have
, from here р = ħ/r. Electron energy in a hydrogen atom

(3.2)

We'll find r, at which energy E minimal. Let us differentiate (3.2) and equate the derivative to zero:

,

We discarded the numerical factors in this expression. From here
- radius of the atom (radius of the first Bohr orbit). For energy we have

One might think that with the help of a microscope it would be possible to determine the position of a particle and thereby overthrow the uncertainty principle. However, a microscope will make it possible to determine the position of the particle in best case scenario accurate to the wavelength of the light used, i.e. Δ x ≈ λ, but because Δ R= 0, then Δ RΔ X= 0 and the uncertainty principle is not satisfied?! Is it so?

We use light, and light, according to quantum theory, consists of photons with momentum p =k/λ . To detect a particle, at least one of the photons of the light beam must be scattered or absorbed by it. Consequently, momentum will be transferred to the particle, at least reaching h/λ . Thus, at the moment of observation of a particle with coordinate uncertainty Δ x ≈ λ the momentum uncertainty must be Δ p ≥h/λ .

Multiplying these uncertainties, we get:

–

the uncertainty principle is satisfied.

The process of interaction of the device with the object being studied is called measurement. This process occurs in space and time. There is an important difference between the interaction of a device with macro- and micro-objects. The interaction of a device with a macro-object is the interaction of two macro-objects, which is quite accurately described by the laws of classical physics. In this case, we can assume that the device has no influence on the measured object, or that the influence is small. When the device interacts with microobjects, a different situation arises. The process of fixing a certain position of a microparticle introduces a change in its momentum that cannot be made equal to zero:

Δ R X ≥ ħ/ Δ X.

Therefore, the impact of the device on the microparticle cannot be considered small and insignificant; the device changes the state of the microobject - as a result of the measurement, certain classical characteristics of the particle (momentum, etc.) turn out to be specified only within the framework limited by the uncertainty relation.

3.3. Schrödinger equation

In 1926, Schrödinger obtained his famous equation. This is the fundamental equation of quantum mechanics, the basic assumption on which all quantum mechanics is based. All the consequences arising from this equation are consistent with experience - this is its confirmation.

The probabilistic (statistical) interpretation of de Broglie waves and the uncertainty relation indicate that the equation of motion in quantum mechanics must be such that it allows us to explain the experimentally observed wave properties of particles. The position of a particle in space at a given moment in time is determined in quantum mechanics by specifying the wave function
(x, y, z, t), or rather the square of the modulus of this quantity.
is the probability of finding a particle at a point x, y, z at a point in time t. The fundamental equation of quantum mechanics must be an equation with respect to the function
(x, y, z, t). Further, this equation must be a wave equation; experiments on the diffraction of microparticles, confirming their wave nature, must derive their explanation from it.

The Schrödinger equation has the following form:

. (3.3)

Where m– particle mass, i– imaginary unit,
– Laplace operator,
,U– particle potential energy operator.

The form of the Ψ-function is determined by the function U, i.e. the nature of the forces acting on the particle. If the force field is stationary, then the solution to the equation has the form:

, (3.4)

Where E is the total energy of the particle, it remains constant in each state, E=const.

Equation (3.4) is called the Schrödinger equation for stationary states. It can also be written in the form:

.

This equation is applicable to non-relativistic systems provided that the probability distribution does not change over time, i.e. when functions ψ look like standing waves.

The Schrödinger equation can be obtained as follows.

Let's consider the one-dimensional case - a freely moving particle along the axis X. It corresponds to a plane de Broglie wave:

,

But
, That's why
. Let us differentiate this expression by t:

.

Let us now find the second derivative of the psi function with respect to the coordinate

,

In non-relativistic classical mechanics, energy and momentum are related by the relation:
Where E- kinetic energy. The particle moves freely, its potential energy U= 0, and full E=E k. That's why

,

is the Schrödinger equation for a free particle.

If a particle moves in a force field, then E– all energy (both kinetic and potential), therefore:

,

then we get
, or
,

and finally

This is the Schrödinger equation.

The above reasoning is not a derivation of the Schrödinger equation, but an example of how this equation can be established. The Schrödinger equation itself is postulated.

In expression

the left side denotes the Hamiltonian operator – the Hamiltonian is the sum of the operators
And U. The Hamiltonian is an energy operator. We will talk in detail about operators of physical quantities later. (The operator expresses some action under the function ψ , which is under the operator sign). Taking into account the above we have:

.

It does not have a physical meaning ψ -function, and the square of its modulus, which determines the probability density of finding a particle in a given location in space. Quantum mechanics makes statistical sense. It does not allow one to determine the location of a particle in space or the trajectory along which the particle moves. The psi function only gives the probability with which a particle can be detected at a given point in space. In this regard, the psi function must satisfy the following conditions:

It must be unambiguous, continuous and finite, because determines the state of the particle;

It must have a continuous and finite derivative;

Function I ψ I 2 must be integrable, i.e. integral

must be finite because it determines the probability of detecting a particle.

Integral

,

This is the normalization condition. It means that the probability that a particle is located at any point in space is equal to one.

Wave function and its physical meaning.

What physical meaning should be given to the wave function we introduced?

We have already discussed this issue and came to the conclusion that this field determines the probability of detecting a particle at various points in space at a given point in time. More precisely, the square of the modulus of the wave function is the probability density of detecting a particle at a point with the coordinate at the moment of time t:

(17.15)

It is natural to believe that somewhere in space a particle reliably exists. By-

Therefore, the wave function must satisfy the following normalization condition

(17.16)

Here the integral is taken over the domain of definition of the wave function, which is usually the entire infinite space. Thus, the states of the particle must be described by functions with an integrable square modulus.

“Trouble” awaits us here. The only wave function we already know is the de Broglie wave, corresponding to a particle with a given momentum value. Because for this wave

ng w:val="EN-US"/>1"> (17.17)

then the normalization integral obviously diverges. On the other hand, such a situation

understandable. If the momentum is known exactly (and for the de Broglie wave this is exactly the case), then from the uncertainty relation for the coordinate uncertainty we obtain

(17.18)

those. the particle is delocalized throughout infinite space. It is precisely this absolutely delocalized state that is defined by a plane wave. Of course, a plane wave has no direct relation to the real state of the particle. This is a mathematical abstraction. Any physical process occurs, perhaps in a macroscopically large, but limited region of space. Therefore, we can assert that the state of a particle with a precisely defined momentum value is fundamentally impossible, and a wave function of the form (17.1) or (17.7) does not describe any state of a real physical object. On the other hand, if the wave packet is wide enough, i.e. its spatial size is much larger than the de Broglie wavelengths of its constituents; the plane wave approximation often turns out to be very convenient from a mathematical point of view.

Thus, in addition to functions with an integrable square modulus in quantum mechanics, it is convenient to work with functions that, according to the normalization condition

(6.16) are not satisfied. Let us consider the issue of normalization of such functions using the example of state (6.1). For simplicity, we again limit ourselves to the one-dimensional case. We assume that the state is in the form of a plane wave

(17.19)

(A= - normalization constant, index " p" indicates that this is a state with an impulse p) given on the segment x∈(− L/ 2, L/ 2). We believe that L is large and in the future we will move to the limit L→∞.

Consider the value of the following integral

(17.20)

Calculating the integral (17.20) gives

Here Δ k= (p− p") h. At Δ k≠ 0 in the limit L→∞ we get that I→0, i.e. wave functions of states with different meanings impulses become orthogonal to each other. In the case of Δ k≡ 0 we get that I= 1 for any finite arbitrarily of great importance L, i.e. the normalization condition (17.16) turns out to be satisfied. This procedure can be used to solve specific problems, but it is not entirely convenient, since the normalization dimension has appeared in the original function (17.19) L. Therefore, they usually do things a little differently. Let the normalization constant A= 1. Then the calculation of integral (17.21) in the limit L→∞ gives

Here we used the well-known relations

This gives rise to the normalization condition for the δ function:

Where (17.23)

In the three-dimensional case we similarly obtain (17.24)

and (17.25)

The normalization condition to the δ function is used in quantum theory whenever

the wave function cannot be normalized according to condition (17.16).

Frank-Hertz experiment

Frank-Hertz experiment- an experience that provided experimental evidence of the discreteness of the internal energy of an atom. Staged in 1913 by J. Frank and G. Hertz.

The figure shows a diagram of the experiment. To cathode TO and grid C 1 electric vacuum tube filled with Hg (mercury) vapor, a potential difference is applied V, accelerating electrons, and the current-voltage characteristic is removed. To the grid C 2 and anode A a retarding potential difference is applied. Electrons accelerated in region I experience collisions with Hg atoms in region II. If the energy of the electrons after the collision is sufficient to overcome the retarding potential in region III, then they will fall on the anode. Consequently, the readings of the galvanometer G depend on the loss of energy by electrons upon impact.

In the experiment, a monotonous increase in current was observed I with increasing accelerating voltage up to 4.9 V, that is, electrons with energy E < 4,9 эВ испытывали упругие соударения с атомами Hg, и внутренняя энергия атомов не менялась. При значении V= 4.9 V (and multiples of it 9.8 V, 14.7 V) sharp drops in current appeared. This definitely indicated that at these values V collisions of electrons with atoms are inelastic in nature, that is, the electron energy is sufficient to excite Hg atoms. At multiples of 4.9 eV energy values, electrons can experience inelastic collisions several times.

Thus, the Frank-Hertz experiment showed that the spectrum of energy absorbed by an atom is not continuous, but discrete, the minimum portion (quantum electromagnetic field) that an Hg atom can absorb is 4.9 eV. The wavelength λ = 253.7 nm of the glow of Hg vapor, which occurred when V> 4.9 V, turned out to be in accordance with Bohr’s second postulate

Pauli's principle.

At first glance, it seems that in an atom all electrons should fill the level with the lowest possible energy. Experience shows that this is not so.

Indeed, in accordance with the Pauli principle, in an atom there cannot be electrons with same values mi of all four quantum numbers.
Each value of the principal quantum number P corresponds 2P 2 states differing from each other in the values ​​of quantum numbers l, m And m S.

A set of electrons in an atom with identical quantum number values P forms the so-called shell. According to the number P

Table 18. 1

Shells are divided into subshells, differing in quantum number l. The number of states in a subshell is 2(2 l + 1).
Different states in the subshell differ in quantum number values T And m S .

Table 18.2

Understanding periodic table elements is based on the idea of ​​the shell structure of the electron cloud of an atom.

Each subsequent atom is obtained from the previous one by adding one unit of nuclear charge ( e) and the addition of one electron, which is placed in the state with the lowest energy allowed by the Pauli principle.

To describe the particle-wave properties of an electron in quantum mechanics, a wave function is used, which is denoted by the Greek letter psi (T). The main properties of the wave function are:

• at any point in space with coordinates x, y, z it has a certain sign and amplitude: BHd:, at, G);
• squared modulus of the wave function | CHH, y,z)| 2 is equal to the probability of finding a particle in a unit volume, i.e. probability density.

The probability density of detecting an electron at various distances from the nucleus of an atom is depicted in several ways. It is often characterized by the number of points per unit volume (Fig. 9.1, A). A dotted probability density image resembles a cloud. Speaking about the electron cloud, it should be borne in mind that an electron is a particle that simultaneously exhibits both corpuscular and wave

Rice. 9.1.

properties. The probability range for detecting an electron does not have clear boundaries. However, it is possible to select a space where the probability of its detection is high or even maximum.

In Fig. 9.1, A The dashed line indicates a spherical surface within which the probability of detecting an electron is 90%. In Fig. Figure 9.1b shows a contour image of the electron density in a hydrogen atom. The contour closest to the nucleus covers a region of space in which the probability of detecting an electron is 10%, the probability of detecting an electron inside the second contour from the nucleus is 20%, inside the third - 30%, etc. In Fig. 9.1, the electron cloud is depicted as a spherical surface, within which the probability of detecting an electron is 90%.

Finally, in Fig. 9.1, d and b, shows the probability of detecting an electron Is at different distances in two ways G from the kernel: at the top is a “cut” of this probability passing through the kernel, and at the bottom is the function itself 4lr 2 |U| 2.

Schrödingsr's equation. This fundamental equation quantum mechanics was formulated by the Austrian physicist E. Schrödinger in 1926. It relates the total energy of a particle E, equal to the sum of potential and kinetic energy, potential energy?„, particle mass T and wave function 4*. For one particle, for example an electron with mass that is, it looks like this:

From a mathematical point of view, this is an equation with three unknowns: Y, E And?". Solve it, i.e. These unknowns can be found by solving it together with two other equations (three equations are required to find three unknowns). The equations for potential energy and boundary conditions are used as such equations.

The potential energy equation does not contain the wave function V. It describes the interaction of charged particles according to Coulomb’s law. When one electron interacts with a nucleus having a +z charge, the potential energy is equal to

Where g = Y* 2 + y 2+ z 2 .

This is the case of the so-called one-electron atom. In more complex systems, when there are many charged particles, the potential energy equation consists of the sum of the same Coulomb terms.

The boundary condition equation is the expression

It means that the electron wave function tends to zero at large distances from the atomic nucleus.

Solving the Schrödinger equation allows one to find the electron wave function? = (x, y, z) as a function of coordinates. This distribution is called an orbital.

Orbital - it is a wave function defined in space.

A system of equations, including the Schrödinger equations, potential energy and boundary conditions, has not one, but many solutions. Each of the solutions simultaneously includes 4 x = (x, y, G) And E, i.e. describes the electron cloud and its corresponding total energy. Each of the solutions is determined quantum numbers.

The physical meaning of quantum numbers can be understood by considering the oscillations of a string, which result in the formation of a standing wave (Fig. 9.2).

Standing wave length X and string length b related by the equation

The length of a standing wave can only have strictly defined values ​​corresponding to the number P, which only accepts non-negative integer values ​​1,2,3, etc. As is obvious from Fig. 9.2, the number of maxima of the oscillation amplitude, i.e. the shape of a standing wave is uniquely determined by the value P.

Since an electron wave in an atom is a more complex process than a standing wave of a string, the values ​​of the electron wave function are determined not by one, but by four

Rice. 9.2.

four numbers, which are called quantum numbers and are designated by letters P, /, T And s. This set of quantum numbers P, /, T simultaneously correspond to a certain wave function Ch"lDl, and the total energy E„j. Quantum number T at E are not indicated, since in the absence of an external field the electron energy from T does not depend. Quantum number s does not affect any 4 *n xt, not at all E n j.

• , ~ elxv dlxv 62*p
• The symbols --, --- mean the second partial derivatives of the fir1 arcs of the 8z2 H"-function. These are derivatives of the first derivatives. Does the meaning of the first derivative coincide with the tangent of the slope of the function H" from the argument x, y or z on the graphs? = j(x), T =/2(y), H" =/:!(z).

The discovery of the wave properties of microparticles indicated that classical mechanics cannot give correct description behavior of such particles. A theory that covers all the properties of elementary particles must take into account not only their corpuscular properties, but also their wave properties. From the experiments discussed earlier, it follows that a beam of elementary particles has the properties of a plane wave propagating in the direction of the particle speed. In the case of propagation along the axis, this wave process can be described by the de Broglie wave equation (7.43.5):

(7.44.1)

where is the energy and is the momentum of the particle. When propagating in any direction:

(7.44.2)

Let's call the function a wave function and find out its physical meaning by comparing the diffraction of light waves and microparticles.

According to wave concepts of the nature of light, the intensity of the diffraction pattern is proportional to the square of the amplitude of the light wave. According to views photon theory, the intensity is determined by the number of photons hitting a given point in the diffraction pattern. Consequently, the number of photons at a given point in the diffraction pattern is given by the square of the amplitude of the light wave, while for one photon the square of the amplitude determines the probability of the photon hitting a particular point.

The diffraction pattern observed for microparticles is also characterized by an unequal distribution of microparticle fluxes. From the point of view of wave theory, the presence of maxima in the diffraction pattern means that these directions correspond to the highest intensity of de Broglie waves. The intensity is greater where the number of particles is greater. Thus, the diffraction pattern for microparticles is a manifestation of a statistical pattern and we can say that knowledge of the type of de Broglie wave, i.e. Ψ -function allows one to judge the probability of one or another of the possible processes.

So, in quantum mechanics, the state of microparticles is described in a fundamentally new way - using the wave function, which is the main carrier of information about their corpuscular and wave properties. The probability of finding a particle in an element with volume is

(7.44.3)

Magnitude

(7.44.4)

has the meaning of probability density, i.e. determines the probability of finding a particle in a unit volume in the vicinity given point. Thus, it is not the function itself that has a physical meaning, but the square of its module, which sets the intensity of de Broglie waves. The probability of finding a particle at a moment in time in a finite volume, according to the theorem of addition of probabilities, is equal to

(7.44.5)

Since a particle exists, it is sure to be found somewhere in space. The probability of a reliable event is equal to one, then

. (7.44.6)

Expression (7.44.6) is called the probability normalization condition. The wave function characterizing the probability of detecting the action of a microparticle in a volume element must be finite (the probability cannot be greater than one), unambiguous (the probability cannot be an ambiguous value) and continuous (the probability cannot change abruptly).

In the coordinate representation, the wave function depends on the coordinates (or generalized coordinates) of the system. The physical meaning is assigned to the square of its modulus, which is interpreted as the probability density (for discrete spectra - simply the probability) to detect the system in the position described by the coordinates at the moment of time:

Then, in a given quantum state of the system, described by the wave function, we can calculate the probability that a particle will be detected in any region of finite volume configuration space: .

It should also be noted that it is also possible to measure phase differences in the wave function, for example, in the Aharonov-Bohm experiment.

Schrödinger equation- an equation that describes the change in space (in the general case, in configuration space) and in time of the pure state specified by the wave function in Hamiltonian quantum systems. Plays the same in quantum mechanics important role, like the equation of Newton's second law in classical mechanics. It can be called the equation of motion of a quantum particle. Installed by Erwin Schrödinger in 1926.

The Schrödinger equation is intended for spinless particles moving at speeds much lower than the speed of light. In the case of fast particles and particles with spin, its generalizations are used (Klein-Gordon equation, Pauli equation, Dirac equation, etc.)

At the beginning of the 20th century, scientists came to the conclusion that there were a number of discrepancies between the predictions of classical theory and experimental data on atomic structure. The discovery of the Schrödinger equation followed de Broglie's revolutionary assumption that not only light, but also any bodies in general (including any microparticles) have wave properties.

Historically, the final formulation of the Schrödinger equation was preceded by a long period development of physics. It is one of the most important equations in physics that explains physical phenomena. Quantum theory, however, does not require a complete rejection of Newton's laws, but only defines the limits of applicability of classical physics. Therefore, Schrödinger's equation must be consistent with Newton's laws in limiting case. This is confirmed by more deep analysis theories: if the size and mass of a body become macroscopic and the accuracy of tracking its coordinate is much worse than the standard quantum limit, the predictions of quantum and classical theories coincide, because the uncertain path of the object becomes close to the unambiguous trajectory.

Time dependent equation

The most general form of the Schrödinger equation is the form that includes time dependence:

An example of the non-relativistic Schrödinger equation in coordinate representation for a point particle of mass moving in a potential field with potential:

Time-dependent Schrödinger equation

Formulation

General case

In quantum physics, a complex-valued function is introduced that describes the pure state of an object, which is called the wave function. In the most common Copenhagen interpretation, this function is related to the probability of finding an object in one of the pure states (the square of the modulus of the wave function represents the probability density). The behavior of a Hamiltonian system in a pure state is completely described by the wave function.

Having abandoned the description of the motion of a particle using trajectories obtained from the laws of dynamics, and having determined instead the wave function, it is necessary to introduce an equation equivalent to Newton's laws and providing a recipe for finding in particular physical problems. Such an equation is the Schrödinger equation.

Let the wave function be given in n-dimensional configuration space, then at each point with coordinates , at a certain moment in time t it will look like . In this case, the Schrödinger equation will be written as:

where , is Planck’s constant; - the mass of the particle, - the potential energy external to the particle at a point at the moment of time, - the Laplace operator (or Laplacian), is equivalent to the square of the Nabla operator and in the n-dimensional coordinate system has the form:

Question 30 Fundamental physical interactions. The concept of physical vacuum in the modern scientific picture of the world.

Interaction. The entire variety of interactions is divided in the modern physical picture of the world into 4 types: strong, electromagnetic, weak and gravitational. According to modern concepts, all interactions are of an exchange nature, i.e. are realized as a result of the exchange of fundamental particles - carriers of interactions. Each of the interactions is characterized by the so-called interaction constant, which determines its comparative intensity, duration and range of action. Let us briefly consider these interactions.

1. Strong interaction ensures the connection of nucleons in the nucleus. The interaction constant is approximately 10 0, the range of action is about

10 -15, flow time t »10 -23 s. Particles - carriers - p-mesons.

2. Electromagnetic interaction: constant of the order of 10 -2, interaction radius is not limited, interaction time t » 10 -20 s. It is realized between all charged particles. Particle – carrier – photon.

3. Weak interaction associated with all types of b-decay, many decays of elementary particles and the interaction of neutrinos with matter. The interaction constant is about 10 -13, t » 10 -10 s. This interaction, like the strong one, is short-range: the interaction radius is 10 -18 m. (Particle - carrier - vector boson).

4. Gravitational interaction is universal, but is taken into account in the microcosm, since its constant is 10 -38, i.e. of all interactions is the weakest and manifests itself only in the presence of sufficiently large masses. Its range is unlimited, and its time is also unlimited. The exchange nature of gravitational interaction still remains in question, since the hypothetical fundamental particle graviton has not yet been discovered.

Physical vacuum

In quantum physics, the physical vacuum is understood as the lowest (ground) energy state of a quantized field, which has zero momentum, angular momentum and other quantum numbers. Moreover, such a state does not necessarily correspond to emptiness: the field in the lowest state can be, for example, a field of quasiparticles in solid body or even in the nucleus of an atom, where the density is extremely high. A physical vacuum is also called a space completely devoid of matter, filled with a field in this state. This state is not absolute emptiness. Quantum field theory states that, in accordance with the uncertainty principle, virtual particles are constantly born and disappear in the physical vacuum: so-called zero-point field oscillations occur. In some specific field theories, the vacuum may have non-trivial topological properties. In theory, several different vacua may exist, differing in energy density or other physical parameters (depending on the hypotheses and theories used). The degeneracy of the vacuum with spontaneous symmetry breaking leads to the existence of a continuous spectrum of vacuum states that differ from each other in the number of Goldstone bosons. Local energy minima at different meanings any fields that differ in energy from the global minimum are called false vacua; such states are metastable and tend to decay with the release of energy, passing into a true vacuum or into one of the underlying false vacua.

Some of these field theory predictions have already been successfully confirmed by experiment. Thus, the Casimir effect and the Lamb shift of atomic levels are explained by zero-point oscillations of the electromagnetic field in the physical vacuum. Modern physical theories are based on some other ideas about vacuum. For example, the existence of several vacuum states (the false vacua mentioned above) is one of the main foundations of the Big Bang inflationary theory.

31 questions Structural levels of matter. Microworld. Macroworld. Megaworld.

Structural levels of matter

(1) - Characteristic feature matter is its structure, therefore one of the most important tasks of natural science is the study of this structure.

It is currently accepted that the most natural and obvious sign of the structure of matter is the characteristic size of an object at a given level and its mass. In accordance with these ideas, the following levels are distinguished:

(3) - The concept of “microworld” covers fundamental and elementary particles, nuclei, atoms and molecules. The macrocosm is represented by macromolecules, substances in various states of aggregation, living organisms, starting with the elementary unit of living things - cells, man and the products of his activities, i.e. macrobodies. The largest objects (planets, stars, galaxies and their clusters form a megaworld. It is important to realize that there are no hard boundaries between these worlds, and we are only talking about various levels consideration of matter.

For each of the considered main levels, in turn, sublevels can be distinguished, characterized by their own structure and their own organizational characteristics.

The study of matter at its various structural levels requires its own specific means and methods.

Question 32 Evolution of the Universe (Friedmann, Hubble, Gamow) and cosmic microwave background radiation.

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