An electron in an infinite square well of width is prepared in the state = 1 3 _1+ 23 , _2

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

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

Problem

An electron in an infinite square well of width

L=0.30\,\mathrm{nm}

is prepared in the state

\Psi=\frac{1}{\sqrt3}\psi_1+\sqrt{\frac23}\,\psi_2,

where

\psi_n

is the

n

th energy eigenfunction and

E_n=\dfrac{n^2\pi^2\hbar^2}{2mL^2}

, with

m

the electron mass. ((a)) State

P(E_1)

and

P(E_2)

using the Born rule in the energy representation. ((b)) Compute

E_1

in electronvolts, and hence the mean energy

\langle E\rangle

in electronvolts.