Expectation value of angular momentum

Thread starter void19
Start date Oct 23, 2019
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Angular Angular momentum Expectation Expectation value Momentum Quantum mechahnics Value

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SUMMARY

The expectation value of angular momentum in quantum mechanics is defined by the equation ⟨Lx⟩=⟨l,m|Lx|l,m⟩=−iℏ⟨l,m|[Ly,Lz]|l,m⟩. The commutation relation for angular momentum operators is given by [Ly,Lz] = iℏ Lx, indicating that the angular momentum components are interrelated. It is essential to divide by ℏ when calculating the expectation value, although this does not alter the final result. Understanding these relationships is crucial for accurate calculations in quantum mechanics.

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Quantum mechanics fundamentals
Angular momentum operators in quantum mechanics
Commutation relations in quantum mechanics
Understanding of expectation values in quantum states

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Oct 23, 2019

void19

Homework Statement: Express Lx in terms of the commutator of Ly and Lz , show that <Lx>=0 for this particle.

Relevant Equations: [Ly,Lz]=i(hbar)Lx

⟨Lx⟩=⟨l,m|Lx|l,m⟩=−iℏ⟨l,m|[Ly,Lz]|l,m⟩

Last edited: Oct 23, 2019

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Oct 23, 2019

PeroK

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Oct 23, 2019

Antarres

Eh, well the formula you wrote under the picture gives exactly the required result, you just have to figure it out. Maybe expand a bit more. Also, ##[L_y,L_z] = i\hbar L_x##, so you need to divide by ##\hbar##, not multiply. But that doesn't change the result.