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Homework Help: Solve Schroedinger Equation with Mathematica DSolve for given potential

  1. Mar 11, 2010 #1
    1. The problem statement, all variables and given/known data
    I need to solve the Schroedinger equation (Using DSolve in Mathematica) for a potential that is infinite below z=0 and V=mgz for positive z.


    2. Relevant equations
    TISE:
    [itex] \psi \text{''}[z]+\frac{2 m}{\hbar }(\text{En}-V[z])\psi [z]==0 [/itex]



    3. The attempt at a solution
    First I defined the potential as
    [itex]V[z]=\text{Piecewise}[\{\{\infty ,z<0\},\{m g z,z\geq 0\}\}];[/itex]

    Then I told Mathematica to solve the Diffeq
    [itex]\text{DSolve}\left[\left\{\psi \text{''}[z]+\frac{2 m}{\hbar }(\text{En}-V[z])\psi [z]==0,\psi [0]==0,\psi [\infty ]==0\right\},\psi [z],z\right][/itex]

    The error mathematica gave me was
    InverseFunction::ifun: Inverse functions are being used. Values may be lost for multivalued inverses. >>

    I'm not really sure how to get mathematica to give me the solution. I know I need 2 conditions besides the diffeq in order to solve. The only boundary condition that I know to use is that the wavefunction must be zero at z=0 since the potential is infinite there.

    Any ideas on what second boundary condition I should use or any ideas on where I'm going wrong? Thanks
     
    Last edited: Mar 11, 2010
  2. jcsd
  3. Mar 11, 2010 #2

    vela

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    It might be choking, in part, on the infinite potential. You know the wavefunction vanishes there, so try using V(z)=mgz and solve for just z>0.
     
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