5 Angular momentum

Question 1

What is the angular momentum for classical physics?

Answer 1

l = r × p

Question 2

What is the angular momentum operator?

Answer 2

L = R × P
Where R and P are 3D position and momentum operators

Question 3

What are the components for the angular momentum operator?

Answer 3

L_x =YP_Z - ZP_y
etc with x–>y–>z–>x

Question 4

What is the equation for the square of the ang momentum operator?

Answer 4

L² = L_x² + L_y² +L_z²

Question 5

What is the commutator of a position operator with its angular momentum counterpart?

Answer 5

[X,L_x] = 0
etc

Question 6

What is the commutator of a momentum operator with its angular momentum counterpart?

Answer 6

[P_x,L_x] = 0
etc

Question 7

What is the commutator of the squared angular momentum operator with its angular momentum counterpart?

Answer 7

[L²,L_x] = 0
For all components, x,y,z

Question 8

What are the ladder operators for angular momentum?

Answer 8

L₊ = L_x + iL_y
L_- = L_x - iL_y

Question 9

What are the quantum numbers for angular momentum?

Answer 9

l, orbital quantum number
m, magnetic quantum number