1. What Is the Significance of the Wavefunction. What Information Is in the Expression Y*Y?

Problem set

1. What is the significance of the wavefunction. What information is in the expression y*y?

2. Identify which of the following functions are eigenfunctions of the operator d/dx:

a. Aeikx b. sinkx c. k d. hx

If they are an eigenfunction then give the corresponding eigenvalue.

3. Determine the commutator of the operators

a. d/dx and x b. d/dx and x2

4. Normalize the following wavefunctions:

a. sin(npx/l) in the range 0 ≤ x ≤ L

5. What is the physical origin of quantized energy states for a particle confined to move in a one-dimensional box?

6. Suppose an electron is in a 1.5 nm box and the wavefunction, y, that describes it is:

y = 0.19 f1 + 0.98 f2, where f1 and f2 are the energy eigenfunctions of the one dimensional particle in the box. Calculate the average energy of the electron. Remember the eigenvalues of the energy are: En = n2h2/8mL2 where m is the mass of the particle, n is the energy level, and L is the length of the box.

7. For an electron in a box of length 1.0 nm, calculate the energy separation in joules and joules per mole between the levels:

a. n=2 and n=1 b. n=6 and n=5

8. Give the expression for the way you would calculate the expectation (average) value of the momentum for a particle in the state n=1 in a square well potential.

9. What are the most likely locations of a particle in a box of length L in the state n=3?

10. Consider a particle in a cubic box. What is the degeneracy of the level that has an energy three times that of the lowest level?