Which are the experimental bases for the assertion that the so-called “time-dependent Schrödinger Equation” is the correct extension of the "time-independent Schrödinger Equation"?
My personal opinion, explained in THE PHYSICAL ROLE OF "MATTER WAVES", is that the two equations tell us quite different stories, but I hope to receive comments.
In describing the dynamics of isolated spin 1/2 ensemble, the thermal equilibrium density matrix is constructed based on stationary state solutions to the time independant schrodinger equation associated with the problem, the dynamics of the density matrix under free evolution/r.f pulses is given, in rotating reference frame, is given using the liouville equation, which is obtained using the time dependant schrodinger equation, experimentally no discrepancies are found w.r.t non-conformity of the two equations as far as the spin dynamics is concerned.
Do you mean that SPIN makes the difference ?
What is the role of spin in the Davisson-Germer experiment ?
No, i just want to say that Time dependant Schrodinger equation and time independant Schrodinger equation are in conformity as far as spin dynamics of spin systems, scalar coupled or otherwise is concerned.
However, i will definitely try to understand your viewpoint and matter in the cited text you have mentioned,
i wish you the very best for your research on such an intricate and interesting problem.
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