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Schrodinger probability problem

  1. Nov 16, 2004 #1
    Here's my problem:
    Using the normalization constant A=(mw/h*pi)^(1/4) and a = mw/2h, evaluate the probability to find an oscillator in the ground state beyond the classical turning points -A0 and A0. Assume A0= .1nm an k = 1 eV/square nm. The h variables actually represent h/2pi.

    The wave function for the ground state is Ae^(-a*x^2). So the square of the wave function is A^2*e^(-2*a*x^2), which I will integrate as x ranges from .1 to infinity.
    I found A^2 to be 1.0735 nm^-1 and a = 1.8102 nm^-2.
    Subsituting these values and integrating yields .394 (probability of finding the oscillator beyond A0). This seems awfully large. What am I doing wrong? Could I possibly have a problem with units?

    Any help appreciated!
     
  2. jcsd
  3. Nov 18, 2004 #2
    Assuming you have calculated correctly, such large value is possible as you are trying to squeeze to wavefunction in a small space; atomic order. So a wavefunction with such a large curvature leads to a large kinetic energy. As kinetic energy is twice the derivative of "x". With a large kinetic energy this may be possible.
     
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