Question
Transcribed Text
2D harmonic oscillator
Consider a 2D harmonic oscillator which is described by the Hamiltonian
= + 2 k
(1)
where w2 = k/m.
(a) Using your knowledge about the 1D harmonic oscillator define operators âr, al and Ni = atai
for the 2D harmonic oscillator and argue that you can write the Hamiltonian as
A=(N1+N2+1)tww. =
(2)
(b) What are the commutation relations of [ai,aj], [at, af] and [ai, af]?
(c) Consider the wave function of the quantum state a a (0). . Briefly explain what does the
quantum state a1 at a2 at (0) describe and show that it is symmetric under the exchange 1 H
2.
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