Quantum Property Definition

Quantum, in physics, discrete natural unit or packet of energy, charge, angular momentum or other physical properties. Light, for example, which appears in some respects as a continuous electromagnetic wave, is emitted and absorbed at the submicroscopic level in discrete or quantum quantities; And for light of a certain wavelength, the magnitude of all emitted or absorbed quanta is the same in energy and momentum. These particle-like packets of light are called photons, a term also applicable to quanta other forms of electromagnetic energy such as X-rays and gamma rays. Submicroscopic mechanical oscillations in the atomic layers that make up crystals also give up energy and momentum in quanta, or absorb energy and momentum called phonons. Algebraic operations of addition and multiplication can be performed with operators. But unlike ordinary numbers (called c numbers in quantum mechanics), operators are “numbers” (–numbers) for which the multiplication operation is noncommutative. If ̂L and ̂M are two operators, then their action on any vector |Ψ› produces a different vector in a different order; ̂L̂M|Ψ› ≠ ̂M̂L|Ψ›, i.e. ̂L̂M ≠ ̂M̂L. The set ̂L̂M – ̂M̂L is denoted [̂L, ̂M] and is called a switch. Only if both operators can be transposed, i.e. [̂L, ̂M] = 0, can they have common eigenvectors, and therefore only then can the observables ̂L and ̂M simultaneously have (exact) values defined for λ and μ.

In other cases, these quantities do not have simultaneously defined values, and then they are related by the uncertainty principle. It can be shown that if [̂L, ̂M] = c, then Δ̂LΔ̂M > ≥ |c|/2, where Δ̂L and Δ̂M are the mean square deviations from the mean values of the corresponding quantities. multi-body systems; identical particles. The quantum equation of motion for a system of N particles is obtained by generalizing the Schrödinger equation for a single particle. It contains potential energy that depends on the coordinates of all N particles and includes both the effect of an external field on them and the interaction between the particles themselves. The wave function is also a function of the coordinates of all particles. It can be thought of as a wave in 3A dimensional space; Therefore, the visual analogy with the propagation of waves in ordinary space is lost. However, this does not matter as the importance of the wave function as a probability amplitude is known. In this case, the quantum laws of motion approach the classical laws of motion for certain trajectories, just as, under similar conditions, the laws of wave optics become the laws of geometric optics (which describes the propagation of light by means of rays). Equation (22), the condition for a short wavelength de Broglie, means that pL ħ ≫, where pL is of order of magnitude equal to the classical effect on the system.

Under these conditions, the constant ħ can be considered as a very small quantity, i.e. the transformation of the laws of quantum mechanics into classical laws is formally realized as ħ —→ 0. At this limit, all the specific phenomena of quantum mechanics disappear, for example, the probability of the tunnel effect is zero. The relationship between classical mechanics and quantum mechanics is less graphic. It is determined by the existence of another universal constant – Planck`s constant h. The constant h (also called quantum of action) has the action dimensions (energy multiplied by time) and is equal to h = 6.62 × 10−27 erg.sec. (The quantity ħ = h/2π = 1.0545919 × 10−27 erg• sec – Dirac`s constant – is more commonly used in theory; it is also called Planck`s constant.) The criterion of applicability of classical mechanics formally consists of the following: classical mechanics is applicable if, under the conditions of a given problem, the physical quantities with the dimension of action are much larger than ħ (so that ħ can be considered very small). This criterion is explained in more detail in the presentation of the physical principles of quantum mechanics. Thus, it could be experimentally proven that light has corpuscular properties in addition to the known wave properties (which are manifested, for example, in the diffraction of light): it consists, so to speak, of particles – photons. The duality of light and its complex wave-particle nature manifest themselves here. Duality is already present in the formula ε = hv, which makes it impossible to choose one or the other concept: in the left part of the equation, energy is ε for a particle, but in the right part, frequency v is a property of a wave.

A formal logical contradiction appeared: to explain certain phenomena, it was necessary to assume that light has a wave nature, but to explain other phenomena, it must have a corpuscular nature. The resolution of this contradiction led significantly to the development of the physical foundations of quantum mechanics. At one point, radial motion is similar to one-dimensional motion, except that rotation induces centrifugal forces.