# Schrodinger Equation and 1D Box

1. Apr 30, 2014

### Litmus

1. The problem statement, all variables and given/known data

Trying to construct Shrodinger Equation given:
* mass: m

* Boundary Conditions: (potential)
V(x)=-Vo exp(-x/L) for 0<x≤L
V(x)=∞ for x≤0

2. Relevant equations

3. The attempt at a solution

(-h^2 / 2m ) (d^2 ψ / dx^2) + V(x)ψ = E * psi

Not sure how to incorporate step-wise V(x) into above eq.

2. Apr 30, 2014

### Staff: Mentor

Hi Litmus, welcome to PF!

What about $x> L$?

And what can you say about the wave function for $x < 0$?

3. Apr 30, 2014

### vela

Staff Emeritus
You need to solve the Schrodinger equation in each region and then match the solutions at the boundaries. Your book should have examples of how to do this.

4. May 1, 2014

### Litmus

I don't understand. I've given conditions x<0, and x>L it's not specified. Why do we care?

Like this?
(-h^2 / 2m ) (d^2 ψ / dx^2) + [-Vo exp(-x/L) ] ψ = E * psi
(-h^2 / 2m ) (d^2 ψ / dx^2) + ∞ψ = E * psi

Boundary is 0 so:
(-h^2 / 2m ) (d^2 ψ / dx^2) + [-Vo] ψ = E * psi

... how do I proceed?

5. May 2, 2014

### unscientific

The problem can be tackled in the following steps:

1. Use TISE to get a general form of the wavefunction
2. Solve for the constants in the general wavefunction using boundary conditions

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