Particle in 3D Box: Wavefunctions and Energies

[carllacan]

Homework Statement

A particle is constrained by walls that form a cubic box. Obtain the wavecuntions and the energies.

Homework Equations

This is a summary of the solutions: http://quantummechanics.ucsd.edu/ph130a/130_notes/node202.html
Here there is also some info: http://en.wikipedia.org/wiki/Particle_in_a_box#Higher-dimensional_boxes

The Attempt at a Solution

I've managed to obtain the correct solution, but I didn't know how to state the boundary conditions and I had to decide the values of the constants using "intuition".

Could you explain me how would the BC look like in this scenario?

Thank you for your time.

 

[dauto]

Wave function is zero at the walls.

 

[unscientific]

Start off with one dimension, with the boundary condition dauto mentioned, show that $k = \frac{n \pi}{L}$ and the wavefunction must be of the form $sin (kx)$.