Though this question arose in quantum mechanics, i think it should be posted here.(adsbygoogle = window.adsbygoogle || []).push({});

Consider a particle in a well with infinite walls:

[tex]

$i i \frac{\partial \Psi}{\partial t} = -\frac12 \frac{\partial^2 \Psi}{ \partial x^2},\:0<x<a$

[/tex]

but the wall start to squeeze

[tex] $\Psi(x=0,t) \equiv 0$ [/tex]

[tex] $\Psi(x=a-t,t) = 0$ [/tex]

In the beginning the state function is known

[tex] $\Psi(x,t=0) = \varphi(x) [/tex]

What is the method for solving this type of PDE?

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# Time-dependent boundary conditions

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