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The compleness of a basis

  1. Nov 10, 2009 #1
    Dear Physics Forum,

    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
     
  2. jcsd
  3. Nov 10, 2009 #2
    A finite set of functions cannot be complete. So yes, you need to include E>0 eigenfunctions as well.
     
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