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Schrödinger equation

  1. May 28, 2009 #1
    1. The problem statement, all variables and given/known data

    Hey guys.

    I have this problem:

    http://img32.imageshack.us/img32/1561/78854429.jpg [Broken]

    For the first part, I believe that adding those solution is just like adding the two levels of energy they represents and that's way this is not a solution for the equation, I think.

    For the second part, I have no idea.
    Can I please have some help?

    Thanks.


    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 28, 2009 #2

    Hao

    User Avatar

    When in doubt, return to the mathematical expression for the Schrodinger's equation.

    Schrodinger's equation is [tex]\hat H \psi_n = E_n \psi_n[/tex].

    In 1D,
    [tex]\hat H = \frac{\hbar^2}{2 m}\frac{\partial^2}{\partial x^2} + V(x)[/tex]

    As this eigenfunction equation is linear, having the Hamiltonian [tex]\hat H[/tex] act on a superposition of eigenfunctions [tex]\psi_n[/tex] givens a superposition of [tex]\psi_n[/tex] and their corresponding energies.

    A similar principle holds for the next part.
     
  4. May 28, 2009 #3
    Just plug the proposed solution into the Schrödinger's equation and show that it satisfies the equation (both sides are equal).
     
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