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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

4 votes
0 answers
76 views

Reference/Help request for formula $[A,e^{-itB}]$ found in physics thread

I'm wondering if anyone has a rigorous reference or a proof of the formula (2) found in the main answer of this thread on the physics stack exchange. I want to use it but in the case where $A, B$ are …
DerGalaxy's user avatar
2 votes
0 answers
136 views

Sufficient initial conditions for "non-local" PDE

I am studying a problem of the form $$i\, \partial_t \psi(t) = L \psi(t) + \int_0^t U(t-r) \psi(r) \, dr, \qquad \psi(0) = \psi_0,$$ where the evolution occurs in some Hilbert space, $L$ is a self-adj …
DerGalaxy's user avatar