• Support PF! Buy your school textbooks, materials and every day products Here!

Solve Schroedinger Equation with Mathematica DSolve for given potential

  • #1

Homework Statement


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.


Homework Equations


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



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:

Answers and Replies

  • #2
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,620
1,254
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.
 

Related Threads on Solve Schroedinger Equation with Mathematica DSolve for given potential

Replies
2
Views
1K
Replies
5
Views
1K
Replies
3
Views
909
Replies
8
Views
1K
Replies
5
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
2K
Replies
2
Views
4K
Replies
3
Views
1K
Top