Derivation of the non-stationary Schrödinger equation from the stationary one
https://doi.org/10.25205/2541-9447-2023-18-3-104-112
Abstract
A derivation of the time-dependent Schrödinger equation from the time-independent one is considered. Instead of time, the coordinate of an additional degree of freedom, the clock, is introduced into the original time-independent Schrödinger equation. It is shown that the standard time-dependent Schrödinger equation can be obtained for the semiclassical clock only. For elucidation of the physical meaning of the equation obtained in this way, various types of clocks are discussed. In addition, the corresponding equation for the density matrix and formulas for the mean values of operators are derived.
About the Author
N. A. Vinokurov
Budker Institute of Nuclear Physics SB RAS
Russian Federation
Russian Federation
Nikolay A. Vinokurov, Doctor of Physical and Mathematical Sciences, Corresponding Member of
RAS
Novosibirsk
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Review
For citations:
Vinokurov N.A. Derivation of the non-stationary Schrödinger equation from the stationary one. SIBERIAN JOURNAL OF PHYSICS. 2023;18(3):104-112. (In Russ.) https://doi.org/10.25205/2541-9447-2023-18-3-104-112
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