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**Unformatted text preview: **re commutator , since , since
1 1 is the eigenvalue of , so ∝ eigenvalue operator eigenfunction
In fact, About Problem 5-40 is a function of some sort 1/2 substitute number operator form of 1/2
adding zero in the form of 1/2
, 1/2 pick out commutator 1/2 since 1 1/2 1/2 , since 1/2 factor out
eigenvalue is one more than that of
eigenfunction
eigenvalue
∝ eigenvalue operator eigenfunction has
, therefore Simpler way
Add zero in the form
, 1st and 3rd term are commutator
since , since
1 1 is the eigenvalue of , so ∝ In fact,
1 2 9/27/2013 Number Operator
Lowering Operator
1 Raising Operator Check these Results since
1 since Raising and Lowering Operators for of Harmonic Oscillator Lowering Operator Recall ̂
̂ Raising Operator Write the position operator in terms of the raising and lowering operators. ̂ ̂ 2 solve for 2 ∗ ∗ 2
∗ 2 ∗ 2
∗ 1 ∗ 1 2 , , 0 Selection Rules
Transitions fro...

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