Problem 2: A particle of mass m in an infinite square well of width a starts out in an equal superposition of the two lowest energy states.

1. Write down Ψ(x, 0) (properly normalized) in terms of a, m, and the relevant constants.
2. Find Ψ(x, t) and its square, and simplify it (the square) to be expressed as some trigonometric function of time (i.e., without complex exponentials).
3. Find the expectation value of the position operator and describe its time dependence.
4. If you measure the particle's energy, what value(s) will you find, and if there is more than one value, then with what probabilities?

Views: 5,481 students