This is a quantum mechanics problem, but the problem itself is reduced (naturally) to a differential equations problem.(adsbygoogle = window.adsbygoogle || []).push({});

I have to solve the following equation:

[tex]\frac{\partial}{\partial t}\psi (x,t) = i\sigma \psi (x,t)[/tex]

where [itex]\sigma > 0[/itex]

The initial condition is:

[tex]\psi (x,0) = \sqrt{\frac{2}{L_0}}\sin \left(\frac{n\pi x}{L_0}\right)[/tex]

and the boundary conditions are:

[tex]\psi (0,t) = \psi(L(t),t) = 0[/tex]

where [itex]L(t)[/itex] is a smooth function with [itex]L(0)=L_0[/itex].

I don't even know how to begin :uhh:. Any ideas?

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# PDE - Boundary value problem found in QM

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