A harmonic oscillator with level spacing is prepared in the state | = 1 2 (|0 +i|1 )

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

A harmonic oscillator with level spacing

\hbar\omega=0.30\,\mathrm{eV}

is prepared in the state

|\psi\rangle=\frac{1}{\sqrt2}\big(|0\rangle+i|1\rangle\big),

where

|n\rangle

is the

n

th energy eigenstate with energy

E_n=\left(n+\tfrac12\right)\hbar\omega

. ((a)) Give

P(E_0)

and

P(E_1)

from the Born rule in the energy representation. ((b)) Compute the mean energy

\langle H\rangle

in electronvolts.