Introduction to Quantum Mechanics · Problem 3.34

Formalism — David J. Griffiths

Physics — Quantum Mechanics · momentum_space_wave_function

Problem

(a) Find the momentum-space wave function

\Phi_n(p, t)

for the

n

th stationary state of the infinite square well. (b) Find the probability density

|\Phi_n(p, t)|^2

. Graph this function, for

n = 1

n = 2

n = 5

, and

n = 10

. What are the most probable values of

p

, for large

n

? Is this what you would have expected? Compare your answer to Problem 3.10. (c) Use

\Phi_n(p, t)

to calculate the expectation value of

p^2

, in the

n

th state. Compare your answer to Problem 2.4.