In spherical coordinates, the ladder operators for orbital angular momentum are of the form: +i cot 0- = e-io +i cot 0- Show, by explicit calculation of the relevant products, that these operators satisfy the commutation relations 1. [L,, L4] = +L4 2. [L?, L4] = 0. 3. [L4, L-] = 2L,.
In spherical coordinates, the ladder operators for orbital angular momentum are of the form: +i cot 0- = e-io +i cot 0- Show, by explicit calculation of the relevant products, that these operators satisfy the commutation relations 1. [L,, L4] = +L4 2. [L?, L4] = 0. 3. [L4, L-] = 2L,.
Related questions
Question
![In spherical coordinates, the ladder operators for orbital angular momentum are of the
form:
eig
+icot θ
= e-io
+i cot 0-
Show, by explicit calculation of the relevant products, that these operators satisfy the
commutation relations
1. [L,, L4] = ±L+
2. [L?, L4] =
0.
3. [L4, L-] = 2L.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdddd2283-0583-4893-a608-c540fd19aa86%2Fd0ef701e-2244-4461-a006-a6c617a2e831%2Fllgzjhh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In spherical coordinates, the ladder operators for orbital angular momentum are of the
form:
eig
+icot θ
= e-io
+i cot 0-
Show, by explicit calculation of the relevant products, that these operators satisfy the
commutation relations
1. [L,, L4] = ±L+
2. [L?, L4] =
0.
3. [L4, L-] = 2L.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
