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We know that for an infinite well of length a, eigenfunctions of the hamiltonian are :

[tex]\psi_n(x)=\sqrt{\frac{2}{a}}sin(\frac{\pi n x}{a})[/tex] related to the eigenvalues [tex]E_n=n^2\frac{\hbar ^2 \pi^2}{2ma^2}[/tex]

Now, I would like to consider two infinite quantum wells of length a et b (not necessarily equal) , like http://photonicssociety.org/newsletters/jun97/art/quantum3.gif [Broken].

The eigenfunctions of the hamiltonian are clearly of the kind [tex]\psi_n^{(a_{well})}(x) + \psi_p^{(b_{well})}(x) [/tex] (n and p are not necessarily equal). But then, how could I find the (n,p) such that these are eigenfunctions. And then, what would be the eigenvalues ?

I thank you in advance for your help.

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# Double asymmetric quantum well

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