Commutator (5 min)

Next: Hamiltonian (10 min) Up: Ladder Operators and Phonons Previous: Ladder Operators and Phonons Contents

Commutator (5 min)

Define

$\displaystyle a:=\sqrt{\frac{m\omega}{2\hbar}}\hat{x}+\frac{i}{\sqrt{2m\hbar\om... ...^+:=\sqrt{\frac{m\omega}{2\hbar}}\hat{x}-\frac{i}{\sqrt{2m\hbar\omega}}\hat{p}.$

(37)

and show that

$\displaystyle [a,a^+] = 1.$

(38)

Tobias Brandes 2004-02-04