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Meden Agan
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- TL;DR Summary
- Implications of difference between Schrödinger equation and the classical wave equation.
Not an expert in QM.
AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order.
But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical.
When deriving the classical wave equation for entities such as the electric and magnetic fields, we consider the oscillation of the electric and magnetic fields. Similarly, why did Schrödinger not derive the wave equation for the physical oscillation of an electron? How did he know that there is no physical oscillation in the electron and that it is only a matter of probability, given that AFAIK the probabilistic interpretation of the wave function came two years after his equation?
AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order.
But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical.
When deriving the classical wave equation for entities such as the electric and magnetic fields, we consider the oscillation of the electric and magnetic fields. Similarly, why did Schrödinger not derive the wave equation for the physical oscillation of an electron? How did he know that there is no physical oscillation in the electron and that it is only a matter of probability, given that AFAIK the probabilistic interpretation of the wave function came two years after his equation?
