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
Classical Angular Momentum p r
Quantum Mechanical Angular Momentum
Commutation Properties
Commutation Properties
Commutation Properties
Quantum Mechanical Angular Momentum Can measure one component and magnitude simultaneously
Spherical Polar Coordinates
Spherical Polar Coordinates Chain rule
Spherical Polar Coordinates
Spherical Polar Coordinates Do not depend on r
Ladder Operators
Ladder Operators Produces new eigenfunction with eigenvalue Step-up operator Produces new eigenfunction with eigenvalue Step-down operator
Ladder Operators commute
Eigenvalues/Eigenfunctions
Eigenvalues/Eigenfunctions For a given a there is a max and min b
Eigenvalues/Eigenfunctions Eigenvalues of Lz are symmetric about 0 ^ n even n odd Not physically meaningful
Spherical Harmonics Find eigenfunctions same way as for Harmonic Oscillator
Legendre Polynomials /Associated Legendre functions
Legendre Polynomials /Associated Legendre functions
Legendre Polynomials /Associated Legendre functions
Spherical Harmonics
Rigid Rotator m1 m2 R r1 r2 Eigenfunctions are spherical harmonics
Rigid Rotator