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Qm tise

  1. Mar 31, 2009 #1
    1. The problem statement, all variables and given/known data
    an electron moves in 1D and is confined to the right half (x>0)
    potential: V(x) = -(e^2)/(8piEx) E is the permittivity of free space
    the ground state wave function is Nxe^(-ax)
    N is normalization constant, and a is another constant needed to be determined


    2. Relevant equations
    time independent schrodinger: (-h^2/2m) (d^2Si/dx^2) + V*Si = E*Si


    3. The attempt at a solution

    The first part of this problem tells my to substitute the ground state wave function in the appropriate TISE to determine a.

    I am completely lost on this one because I usually substitute V(x) into the TISE to determine a and I never had to do it the way they are describing. I tried to sub the wave function into the standard TISE and got:

    (ax+2)/a^2 = (E-V)(-2xm)/(h^2) - this is after doing the double derivative of the wave function etc.

    However I still cant solver for just a doing the way I tried.
    Please help, thanks.
     
  2. jcsd
  3. Mar 31, 2009 #2

    CompuChip

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    Homework Helper

    Why can't you do that here? V(x) is given, it is V(x) = -(e^2)/(8piEx) according to you. Also, psi is given. If you plug it in you will get an equation containing a's. So it will tell you what a can be such that the given ground state wavefunction is indeed a solution of the TISE for the given potential.
     
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