Answer to Question #94310 in Quantum Mechanics for Glorias

Question

A quantum particle confined to one-dimensional potential well of width ‘a’ is in its
first excited state. What is the probability of finding the particle over an interval of a/4
at the center of the box?

Answer 1

$\psi=\sqrt\frac{2}{a}sin(\frac{\pi nx}{a})$

$n=2$

$W=\int_{\frac{3a}{8}}^{\frac{5a}{8}} |\psi(x)|^2 dx$

$W=\frac{2}{a}\int_{\frac{3a}{8}}^{\frac{5a}{8}} sin^2 (\frac{2\pi x}{a})dx = 0.09$