Question

Angular momentum state of the form |ψ⟩ = |ℓ,0>. Use this state in determining the expectation values of Lx, Lx^2, and determine σLx for this state. Discuss your result, especially the ℓ=0 case. Hint: Use Lx = (L+ + L-)/2 and Ly = -i(L+ - L-)/2. Remember also that L±L∓ = L^2 - Lz^2 ± ħLz.

Name: angular momentum state of the form l0 use this state in determining the expectation values of lx lx2 and determine lx for this state discuss your result especially the l0 case hint use lx l 52755
Uploaded: 2022-06-24T07:10:21-08:00
Duration: 4 min 48 s
Channel: Shyam P
Description: angular momentum state of the form l0 use this state in determining the expectation values of lx lx2 and determine lx for this state discuss your result especially the l0 case hint use lx l 52755

          Angular momentum state of the form |ψ⟩ = |ℓ,0>.
Use this state in determining the expectation values of Lx, Lx^2, and determine σLx for this state. Discuss your result, especially the ℓ=0 case.
Hint: Use Lx = (L+ + L-)/2 and Ly = -i(L+ - L-)/2.
Remember also that L±L∓ = L^2 - Lz^2 ± ħLz.

Added by Joel B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Shyam P

06/24/2022

Step 1

We know that Lx = (L+ + L-)/2, where L+ and L- are the ladder operators for the angular momentum. Using the expression for L± = L∓ = L^2 - Lz^2 ± ħLz, we can rewrite Lx as: Lx = (L^2 - Lz^2 + ħLz + L^2 - Lz^2 - ħLz)/2 = (2L^2 - 2Lz^2)/2 = L^2 - Lz^2 Now, Show more…

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Angular momentum state of the form |ψ⟩ = |ℓ,0>. Use this state in determining the expectation values of Lx, Lx^2, and determine σLx for this state. Discuss your result, especially the ℓ=0 case. Hint: Use Lx = (L+ + L-)/2 and Ly = -i(L+ - L-)/2. Remember also that L±L∓ = L^2 - Lz^2 ± ħLz.