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Partial differential equation which describes the time evolution of the wavefunction of a quantum system. It is one of the first and most fundamental equations of quantum mechanics.
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Why does it matter that the propagator is related to the Green's function for the Schrodinge...
If $L = i \hbar \hat{H} - \dfrac{d}{dt}$, then $ L \psi(x,t) = 0$ is the Schrodinger equation.
It is well known that we can solve the Schrodinger equation with initial condition $\psi(x,0) = f(x)$ wi …
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Feynman's derivation of the Schroedinger equation by expanding path integrals to first order...
As discussed in the answer to How can one derive Schrödinger equation?, one should be able to "derive" the Schrodinger equation from the path integral formulation of quantum mechanics.
However, as no …