angmomcommutation - Quantum Mechanics: Commutation Relation...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Quantum Mechanics: Commutation Relation Proofs 5th April 2010 I. Proof for Non-Commutativity of Indivdual Quantum Angular Momentum Operators In this section, we will show that the operators L x , L y , L z do not commute with one another, and hence cannot be known simultaneously. The relations are (reiterating from previous lectures): L x =- i h y z- z y L y =- i h z x- x z L z =- i h x y- y x We would like to proove the following commutation relations: [ L x , L y ] = i h L z , [ L y , L z ] = i h L x , [ L z , L x ] = i h L y . We will use the first relation for our proof; the second and third follow analo- gously. Lets also consider a function, f ( x, y, z ) that we will have the opera- tors act upon in our discussion. The expanded version of [ L x , L y ] = i h L z is: [ L x , L y ] = L x L y- L y L x 1 = y z- z y z x- x z...
View Full Document

Page1 / 3

angmomcommutation - Quantum Mechanics: Commutation Relation...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online