Angular Momentum in Quantum Mechanics
In this video we start with the classical definition of angular momentum and as position and momentum are operators in quantum mechanics, we replace x and p with their corresponding operators to find the expressions for angular momentum. Then we find a lot of commutation relations for the angular momentum operators with each other and also with position and momentum operators.
By using these commutation relations and also introducing raising and lowering operators, we can find the eigenvalues of angular momentum without finding the eigenfunctions.
In the following videos I'm going to find the eigenfunctions and also show you how they are shown in matrix form.
00:00 Angular Momentum definition and commutation relations
11:34 General angular momentum (J)
14:13 Raising and Lowering operators
18:41 Eigenvalues of angular momentum
25:20 How do raising and lowering operators change the eigenfunctions of Jz