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7.1 Exercise 2

Avg difficulty 2.5

Suppose that a particle with energy E is moving along the x-axis and is confined in the region between 0 and L. One possible wave function is

ψ(x,t)={Ae−iEt/ℏsinπxL,when0≤x≤L0,otherwise.\psi \left(x , t\right) = \left\{\right. \begin{aligned}A e^{− i E t / \hbar} \text{sin} \frac{\pi x}{L} , & \text{when} 0 \leq x \leq L \\ 0 , & \text{otherwise}\end{aligned} .

Determine the normalization constant.

OpenStax University Physics Volume 3, 7.1 Wave Functions, exercise 2

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Adapted from University Physics Volume 3 © 2016 Rice University. Licensed under CC BY 4.0. Source: University Physics Volume 3. Imported at revision db44eb9.