10_HO_raising_lowering [Read-Only]

Add zero in form of 1st and 3rd term are commutator

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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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This document was uploaded on 01/19/2014.

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