At one instant a particle is described by (x) = cases A ( x/L) & 00 A$ real and positive.

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · Wave mechanics in one dimension

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The Schrödinger equation and the Born rule

Problem

At one instant a particle is described by

\Psi(x) = \begin{cases}A\sin(\pi x/L) & 0<x<L\\ 0 & \text{otherwise}\end{cases}

for some length

L>0

, with

A

real and positive. ((a)) Find

A

. ((b)) Find the probability that the particle is found in the middle half of the region,

L/4 < x < 3L/4