- #1
Hertz
- 180
- 8
Homework Statement
Given [itex]\Psi(x, y, z)=(2/L)^{3/2}sin(\frac{n_x\pi x}{L})sin(\frac{n_y\pi y}{L})sin(\frac{n_z\pi z}{L})[/itex], calculate the first few energy levels and tell which are degenerate.
The Attempt at a Solution
I don't have much of an attempt to be honest.. What I've done so far is find the Energy Operator [itex]\hat{E}=i\hbar \frac{\partial}{\partial t}[/itex], however, I quickly realized this wouldn't help because my wave function is not time dependent. Next, I realized that this particle has no potential energy (this is an infinite well problem), so [itex]E=\frac{p^2}{2m}[/itex], and [itex]p=\frac{\hbar}{\lambda}[/itex]. However, I also don't know how to calculate lambda and I'm not even sure that I'm headed in the right direction >.<
I've seen other formulas for energy levels of a particle. Of course, my teacher went through this in class (unfortunately the class has trouble keeping up with him). The problem is, I don't know if those formulas apply to this specific wave function, and furthermore, I should be able to do this from scratch myself, so that's my aim. Any help is appreciated.
edit-
From a few things I posted above:
[itex]E=\frac{\hbar^2}{2m\lambda^2}[/itex]
Since there are multiple wavelengths, (in each of the three degrees of freedom), can I say:
[itex]E=\sum{\frac{\hbar^2}{2m\lambda^{2}_{i}}}[/itex]