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Schrodinger Equation Preserves Normalization

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data
    Show that the time dependent Schrodinger equation preserves the normalization of the wavefunction

    2. The attempt at a solution
    I don't need help showing this, I'm just not too sure what the question is asking. Do I just show that if a normalized wave-function [itex] \psi [/itex] is a solution to the TDSE, then the TDSE doesn't change the normalization? That is, assuming that U(t) is the time evolution operator [itex] U(t) = \displaystyle e^{-\frac{i}{\hbar} Ht } [/itex] do I just show that [itex] \int_V |U(t) \psi|^2 dV [/itex] is also normalized? (which should follow pretty easily since U(t) is unitary).
     
  2. jcsd
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