Simple Nature - Light and Matter

Exercise 13B: Choice of quantum numbers

We could choose to identify a human by their first and last names, or by their social security
number. We’re free to choose any set of labels, as long as they’re compatible.

1. Warm-up, nothing to do with quantum mechanics:

Express thex′,y′coordinates in terms of thex,ycoordinates:

x′= x+ y

y′= x+ y

2. Consider these four`= 1 wavefunctions on the “quantum moat:”

Ψ = eiθ Ψ= e−iθ

Ψs= sinθ Ψc= cosθ

Determine the normalization factor for your group’s wave.

3. We now want to discuss the standing waves in terms of the traveling waves:

Ψc= Ψ + Ψ

Ψs= Ψ + Ψ.

Determine the coefficients assigned to your group, and check your equation at the value ofθ

assigned to your group:θ= 0,π/2,π, or 3π/2.

4. An electron is initially in state Ψc, and Jane then measures its angular momentum. Dis-
   cuss what happens to the electron’s wavefunction and to Jane’s, as in sec. 13.2.4, p. 885, on
   entanglement.


5. Discuss the probability interpretation and normalization.

Exercises 953