Solving the Schrödinger Equation: Need Help!

[asi123]

Homework Statement

Hey guys.

I have this problem:

http://img32.imageshack.us/img32/1561/78854429.jpg

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.

Homework Equations

The Attempt at a Solution

 

[Hao]

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

Schrödinger'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.

 

[phsopher]

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