Chapter 7, Problem 24E

(a)

To determine

The derivation for the formula $\psi \left(x,y\right)=f\left(x\right)g\left(y\right)$ .

(b)

To determine

The form of $f\left(x\right)$ and $g\left(y\right)$ outside the well, the function that would be acceptable standing wave equation $f\left(x\right)$ and $g\left(y\right)$ inside the well. Determine if $C_x$ and $C_y$ are positive or negative or zero also determine their values.

(c)

To determine

The number of independent quantum numbers.

(d)

To determine

The expression for the allowed energies.

(e)

To determine

Whether there are energies that don’t have unique corresponding wave function.