The Real Product: Particle in a 3-Dimensional Box

We show that the product of one-dimensional functions is indeed a solution to the 3-dimensional problem. We find the energy and show that the energy and wavefunction now depend on 3 independent quantum numbers. When the box is symmetric, for example, a cube, some energy levels are degenerate. We noted that symmetry generally leads to degeneracy, though not all degeneracy is a result of symmetry (accidental symmetry). We extended the concept of the product wavefunction to systems of more than one particle. We drew a quick concept map of where we have been in the course so far.

MP3 podcast
screencast
Mathematica notebook - same as previous lecture

---

Trout Fishing in America - the band
Six

What do you get when you add three plus three?
I believe the answer is six.
And how ‘bout seven when take away one now?
I believe the answer is six.

Well, how do you do that in your head?
I would need a pencil all filled with lead,
A huge piece of paper ‘bout the size of my bed.
Now…You must be a mathematician.....

and on...to

What is the dimension of the field of complex numbers over
the real numbers, times the order of the alternating group on
three elements divided by the definite integral from zero to pi
over two of sine of X D X?