Harmonic and Annihilation Operators
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An important set of operators that are often used in discussing the harmonic oscillator are the creation and annihilation operators a and a^t.
a = (1/ (2^(1/2)) )(X + iP)
a^t = (1/ (2^(1/2)) )(X - iP)
X and P are the coordinate and the conjugate momentum so that
[X,P] = i©¤
1. Show that a is not a Hermitian operator
2. Find [a, a^t]
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Solution Summary
This solution shows that certain variables are not Hermitian operators.
Solution Preview
Recall that both X and P are Hermitian, so
a* = (1/ (2^(1/2)) )(X* - iP*) = a = ...
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