Dear Physics Forum,(adsbygoogle = window.adsbygoogle || []).push({});

I have a question about quantum mechanics.

I know that the solutions of a Hamiltonian will form a complete basis.

However, for a case of a finite well, in the region of bound states (E<0), the number of eigenfunctions is finite, I wonder that they are enough to form a complete basis or not?

For the case of infinite square well or Hydrogen potential, the basis is complete.

But for the case of an attractive Delta well, or a finite well, do the bound states form a complete one, or we need to include the wave function for E>0?

Thank you very much.

Bests,

Tung LE

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# The compleness of a basis

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