# Homework Help: Solving a time independent Schrodinger equation

1. Mar 31, 2012

### collpitt

1. The problem statement, all variables and given/known data
Hello!
I am currently stuck with a time independent Schrodinger equation where the potential "V(x)" is hyperbolic in nature. I was wondering if any one could give me a hint as to how I should approach this problem in order to get an analytical solution (without using numerical techniques).

2. Relevant equations
The equation is of the form,
d²/dx²(Ѱ) + 2m/ħ²{E + δp²/x(p-x)}(Ѱ) = 0
where the voltage V(x) = -{δp²/x(p-x)}

3. The attempt at a solution
Thank you!

2. Apr 7, 2012

### AuraCrystal

Stupid question: is $\delta$ just a number here?

3. Apr 7, 2012

### collpitt

Yes, δ, E, p are all constants.
I am trying to solve it by defining z = y(x) and changing the differential equation. But it is getting quite complicated. :(

Any help would be gladly appreciated.

4. Apr 8, 2012

### darkxponent

Did u try series solution for diffrntial eqn

5. Apr 8, 2012

### collpitt

Yes. But I am unable to reduce the equation to any of the forms I know (bessel, legendre, laguerre, hermite, chebyshev).

6. Apr 8, 2012

### genericusrnme

I believe the solution is a series, I'll give you a clue; hyper

7. Apr 9, 2012

### collpitt

Yesss!!! Thank you!!! I believe it can be reduced to the hypergeometric form. Thank you very much [bold]genericusrnme[/bold] !!
I will post the solution as soon as I finish.