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Canonical Quantization problem; finding Schroedinget time-dependent equation

  1. Apr 20, 2012 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m is confined in a Pösxhl-Teller potential as defined by:

    V(x) = -V0sech2(αx)

    Where V0 and α are constants representing the depth and width of the well.

    Use canonical quantisation to find the time-depndent Schrödunger equation for a particle in the PT potential.

    2. Relevant equations



    3. The attempt at a solution

    I assumed that I'd be required to Use an operator on this equation and I gathered from various readings that it is related to the Uncertainty Principle.

    ΔxΔp≥(h-bar)/2

    V(x)p(x) = (h-bar)/i d/dx -V0sech2(αx)

    I performed the derivative and didn't get anything useful. I checked it on Wolfram Alpha and my calculus was fine, so I think I'm on the wrong track.

    Am I using the right operator? Am I even supposed to use an operator??

    Guidance would be appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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