For a system, a particle that has a squarewell potential looks like:
Code:
V(x)

  > x
a  a
  
_____ V_0
Tried drawing as best as I could (the center line is an arrow going up that is $\displaystyle V(x)$, and the corners where the horizontal line meets the vertical line is $\displaystyle a$ and $\displaystyle a$ (left and right).) The base is $\displaystyle V_0$.
Questions:
b.) Determine which of the $\displaystyle E$ situations in part a.) has restriction on the allowed energies. Explain what mathematics is the cause of the restriction.

This question is kind of tricky. We know E > 0 usually has reflection and dominates at low energy. The current is same everywhere..
$\displaystyle \frac{\hbar k}{m}(1  R^2) = \frac{\hbar k}{m}T^2$
I'm assuming there's no transmission/reflection?
Eigenvalues (can't be divided, unit has no path). They are discrete.
The bigger $\displaystyle V_0$ is, the more boundary conditions? Always has 1 bound state... that's pretty much where I'm at.