1. Quantum Mechanics of Angular Momentum
Classical Angular Momentum
Quantum Mechanical Angular Momentum
Spherical Polar Coordinates
Ladder Operators
Eigenvalues / Eigenfunctions
Spherical Harmonics
Legendre Polynomials /Associated Legendre functions
Rigid Rotator

2. Classical Angular Momentump r

3. Quantum Mechanical Angular Momentum

4. Commutation Properties

5. Commutation Properties

6. Commutation Properties

7. Quantum Mechanical Angular Momentum
Can measure one component and magnitude simultaneously

8. Spherical Polar Coordinates

9. Spherical Polar Coordinates
Chain rule

10. Spherical Polar Coordinates

11. Spherical Polar Coordinates
Do not depend on r

12. Ladder Operators

13. Ladder Operators Produces new eigenfunction with eigenvalue
Step-up operator
Produces new eigenfunction with eigenvalue
Step-down operator

14. Ladder Operators
commute

15. Eigenvalues/Eigenfunctions

16. Eigenvalues/Eigenfunctions
For a given a there is a max and min b

17. Eigenvalues/Eigenfunctions
Eigenvalues of Lz are symmetric about 0 ^
n even
n odd
Not physically meaningful

18. Spherical Harmonics
Find eigenfunctions same way as for Harmonic Oscillator

19. Legendre Polynomials /Associated Legendre functions

20. Legendre Polynomials /Associated Legendre functions

21. Legendre Polynomials /Associated Legendre functions

22. Spherical Harmonics

23. Rigid Rotator m1 m2 R r1 r2
Eigenfunctions are spherical harmonics

24. Rigid Rotator