Homework Help: Schrödinger equation

1. May 28, 2009

asi123

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

Hey guys.

I have this problem:

http://img32.imageshack.us/img32/1561/78854429.jpg [Broken]

For the first part, I believe that adding those solution is just like adding the two levels of energy they represents and that's way this is not a solution for the equation, I think.

For the second part, I have no idea.
Can I please have some help?

Thanks.

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 4, 2017
2. May 28, 2009

Hao

When in doubt, return to the mathematical expression for the Schrodinger's equation.

Schrodinger's equation is $$\hat H \psi_n = E_n \psi_n$$.

In 1D,
$$\hat H = \frac{\hbar^2}{2 m}\frac{\partial^2}{\partial x^2} + V(x)$$

As this eigenfunction equation is linear, having the Hamiltonian $$\hat H$$ act on a superposition of eigenfunctions $$\psi_n$$ givens a superposition of $$\psi_n$$ and their corresponding energies.

A similar principle holds for the next part.

3. May 28, 2009

phsopher

Just plug the proposed solution into the Schrödinger's equation and show that it satisfies the equation (both sides are equal).