Quantum Physics II, Lecture Notes 9 - MIT OpenCourseWare

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ANGULAR MOMENTUM B. Zwiebach December 16, 2013 Contents 1 Orbital angular momentum and central potentials 1 Quantum mechanical vector identities. . . . . . . . . . . . . . . . . . . . . . . . 2 Properties of angular momentum . . . . . . . . . . . . . . . . . . . . . . . . . . 6 The central potential Hamiltonian. . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Algebraic theory of angular momentum 11 3 Comments on spherical harmonics 18 4 The radial equation 20 5 The free particle and the infinite spherical well 24 Free particle.

In quantum mechanics the classical vectors lr, pl and Ll. become operators. More precisely, they give us triplets of operators: lr → (ˆx, y,ˆ zˆ), lp → ( ˆpx ,pˆy ,pˆz ), (1.3) Ll → (L. ˆ. x ,Lˆy ,Lˆz ). When we want more uniform notation, instead of x, y, and z labels we use 1, 2 and 3 labels:

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