Classical Mechanics and Quantum Mechanics:  An Historic-Axiomatic Approach

Classical Mechanics and Quantum Mechanics: An Historic-Axiomatic Approach

This unique textbook presents a novel, axiomatic pedagogical path from classical to quantum physics. Readers are introduced to the description of classical mechanics, which rests on Euler’s and ...
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Conservation and Change of Stationary States

Pp. 142-150 (9)

Peter Enders

Abstract

The time-independent Schrödinger equation represents a stationary-state equation. The stationary wave functions obtained so far are time independent. Their time-dependence is obtained by means of rather general arguments. Then, stationarystate functions are found. The next step in Newton’s and Euler’s representations of classical mechanics is (to derive) the equation of change of stationary-states. Here, Euler’s principles of stationary-state change are generalized to quantum-mechanical systems. This enables us to derive the quantum-mechanical equation of change of stationary-states. The time-independent Schrödinger equation, i.e, the equation of motion will follow in the next chapter.

Keywords:

Equation of change of stationary-states, Euler’s principles of stationary- state change, Stationary-state functions, Stationary wave function, Timeindependent Schrödinger equation.

Affiliation:

Taraz State Pedagogical University, Kazakhstan.