Answer to Question #78881 in Quantum Mechanics for Vicky

Question

If quantum physics formulas are not applicable at subatomic levels, why do we still use them for deriving relations at the subatomic level ?
Ex. if equations of motions are not applicable at subatomic level , why do we use the equations to explain the path of an electron moving perpendicular to electric field ?

Answer 1

In my opinion, the formulation of the question is incorrect from the very beginning. Quantum Physics (and Quantum Mechanics (QM) in particular) describes behavior and properties of matter on all molecular, atomic and subatomic levels (see definition from [1] and citations therein). For example, the structure of energy levels of any atomic nucleous (which size is 10^(-5) of the size of an atom and which can be treated as a composite subatomic particle), its excitations and relaxation can be described only by means of QM and nothing else.
Moreover, according to the world's famous scientist and lecturer R. Feynman, there is no separation between classical world and quantum world – there exists only quantum world that sometimes can be treated in a classical manner. So the question is about the situations where one can neglect the quantum properties of matter and use much simpler apparatus of classical mechanics (this means that the formulas of QM are still valid, however, their implementation is senseless due to complexity). By the way, this situation is similar to the one regarding the usage of Special Theory of Relativity in mechanics: it is valid for any problem of classical mechanics, however, one should use it only in the cases of big velocities (v ~ c) and can apply much simpler Newtonian theory + Galilean transformation (which is the limit of Special Theory of Relativity) in the case v ≪c. In QM there exists the so-called classical (sometimes its called quasi-classical) [2] where it can be shown (see expression (23.11) of [2] for details) that free particles (which movement is classically infinite) can be described by means of classical mechanics and its equations of motion. The example in the question where the transversal (to the direction of the electric field) movement of an electron is considered can be successfully described by means of simple expressions because in this direction it can be treated as "free".

[1] (Electronic resource) https://en.wikipedia.org/wiki/Quantum_mechanics
[2] A.S.Davydov / Quantum Mechanics (translated, edited and with additions by D.Ter Haar) // Pergamon Press (Oxford, London, Edinburgh, New York, Paris, Frankfurt), 1965.