A Modern Approach to Quantum Mechanics · Problem 6.16

The One-Dimensional Harmonic Oscillator — John S. Townsend

Physics — Quantum Mechanics · sudden-approximation-infinite-well

Problem

A particle of mass mm is in lowest energy (ground) state of the infinite potential energy well V(x)={00<x<L∞elsewhereV(x) = \begin{cases} 0 & 0 < x < L \\ \infty & \text{elsewhere} \end{cases} At time t=0t = 0, the wall located at x=Lx = L is suddenly pulled back to a position at x=2Lx = 2L. This change occurs so rapidly that instantaneously the wave function does not change. (a) Calculate the probability that a measurement of the energy will yield the ground-state energy of the new well. What is the probability that a measurement of the energy will yield the first excited energy of the new well? (b) Describe the procedure you would use to determine the time development of the system. Is the system in a stationary state?

Related theory

Browse the problem library