Introduction to Quantum Mechanics · Problem 2.8

Time-Independent Schrödinger Equation — David J. Griffiths

Physics — Quantum Mechanics · infinite_square_well

Problem

A particle of mass

m

in the infinite square well (of width

a

) starts out in the state

\Psi(x, 0) = \begin{cases} A, & 0 \le x \le a/2, \\ 0, & a/2 \le x \le a, \end{cases}

for some constant

A

, so it is (at

t = 0

) equally likely to be found at any point in the left half of the well. What is the probability that a measurement of the energy (at some later time

t

) would yield the value

\pi^2 \hbar^2 / 2ma^2