Group theory and intrinsic spin; specifically, s=1/2

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Presentation transcript:

Group theory and intrinsic spin; specifically, s=1/2 PHY 745 Group Theory 11-11:50 AM MWF Olin 102 Plan for Lecture 25: Group theory and intrinsic spin; specifically, s=1/2 Dirac equation for hydrogen atom Spin-orbit interaction Double groups 3/24/2017 PHY 745 Spring 2017 -- Lecture 25

3/24/2017 PHY 745 Spring 2017 -- Lecture 25

Dirac equation for describing the quantum mechanics of an electron 3/24/2017 PHY 745 Spring 2017 -- Lecture 25

Other useful four-component matrices: Four-component Dirac Hamiltonian for an electron in a spherically symmetric scalar potential V(r): Other useful four-component matrices: 3/24/2017 PHY 745 Spring 2017 -- Lecture 25

The following commutation relations can be shown: Useful identity: 3/24/2017 PHY 745 Spring 2017 -- Lecture 25

Eigenfunctions of Dirac Hamiltonian for spherical potential Relationships between eigenvalues 3/24/2017 PHY 745 Spring 2017 -- Lecture 25

3/24/2017 PHY 745 Spring 2017 -- Lecture 25

3/24/2017 PHY 745 Spring 2017 -- Lecture 25

3/24/2017 PHY 745 Spring 2017 -- Lecture 25

3/24/2017 PHY 745 Spring 2017 -- Lecture 25

3/24/2017 PHY 745 Spring 2017 -- Lecture 25

3/24/2017 PHY 745 Spring 2017 -- Lecture 25

3/24/2017 PHY 745 Spring 2017 -- Lecture 25

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