An electron is confined to an infinite square well of width

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · Wave mechanics in one dimension

The Structure of Quantum Mechanics, Ch The wave function is not the state

Problem

L

, with walls at

x=0

and

x=L

. It occupies the third energy eigenstate, whose position-representation wave function is

\psi_3(x)=\sqrt{\frac{2}{L}}\sin\!\left(\frac{3\pi x}{L}\right),\qquad 0<x<L.

Using the Born rule in the position representation, compute the probability of finding the electron in the interval

0<x<L/9