An electron sits in an infinite square well of width nm on

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · The formalism of quantum mechanics

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Stationary states and bound states in one dimension

Problem

An electron sits in an infinite square well of width

a = 1.00

nm on

0 < x < a

, with normalised energy eigenfunctions

\psi_n(x) = \sqrt{2/a}\,\sin(n\pi x/a)

and energies

E_n = n^2\pi^2\hbar^2/2m_ea^2

. At

t = 0

its wave function is

\Psi(x,0) = A\left[\psi_1(x) + 2\psi_2(x)\right],

with

A

real and positive. ((a)) Find

A

. ((b)) The energy is measured. What is the probability of obtaining

E_2

? ((c)) Find

\langle H\rangle

for this state, in eV.Use

\hbar^2/2m_e = 0.0381

eV nm

^2