## Physics 4307

### Introduction to Quantum Mechanics

Homework Assignment 5

Due Date: 2:00 p.m. on Thursday, November 12, 2015

- Find all bound state energies for an electron in the symmetric finite well of V(x) =
0 for -L/2 ≤ x ≤ +L/2 with L = 2nm and V(x) = 13.6056923 eV = 1.0
Ryd = 0.5 Eh = 0.5 au elsewhere.
**Plot** the four lowest
stationary state solutions for the well. Compare the lowest four allowed energies
for this well to those of the infinite square well of the same width.
- For the previous finite well problem, what happens to the number of
allowed states as the well becomes narrower (L < 2 nm)? Does the value of the ground state energy change?
If so, how does the ground state energy of the narrower well differ from
that of the 2 nm well?
- What happens to the number of states and the value of the ground state
energy as the original finite well becomes wider (L > 2nm)?
- For the previous finite well problem with L = 2 nm, what happens to the ground state
energy of the well as the walls become harder, i.e., as V(x) increases at
+/- L/2, e.g., for V(x) >> 13.6 eV?
- For the 1-D delta function well: V(x) = -α δ(x) where
α is a positive constant and V(x) = 0 for x ≠ 0. Find the reflection (R) and
transmission (T) coefficients for an E > 0 plane wave incident from the
left.
- For problems 6 and 7, click here.

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