Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
PROBLEM 3. Calculate the following commutator: [L, f(r)], where L is the operator of orbital momentum, and f(r) is a function of the radial coordinate r = Vr2 + y? + z?.

PROBLEM 3. Calculate the following commutator: [L, f(r)], where L is the operator of orbital momentum, and f(r) is a function of the radial coordinate r = Vr2 + y? + z?.

icon
Related questions
Question
PROBLEM 3. Calculate the following commutator: [L, f(r)], where L is the operator of orbital momentum, and f(r) is a function of the radial coordinate r = Vr2 +y2 + z2.
Transcribed Image Text:PROBLEM 3. Calculate the following commutator: [L, f(r)], where L is the operator of orbital momentum, and f(r) is a function of the radial coordinate r = Vr2 +y2 + z2.
Expert Solution
Step 1

Note that the orbital angular momentum operator (L) may be expressed in spherical polar form from the vector product of the radius vector (r) and the linear momentum operator (p) as follows:

 

L^=r×p^=rr^×-iℏ∇=-iℏr^×r^∂∂r+θ^r∂∂θ+φ^rsinθ∂∂φ=-iℏφ^∂∂θ-θ^sinθ∂∂φ                     ∵r^×r^=0, r^×θ^=φ^, r^×φ^=-θ^

 

Note that there is no r dependence in L.

steps

Step by step

Solved in 2 steps

Blurred answer