Physics 451 Quantum mechanics I Fall 2012 Nov 20, 2012 Karine Chesnel
EXAM III Quantum mechanics Time limited: 3 hours Closed book Closed notes Useful formulae provided When: Monday Nov 26 – Fri Nov 30 Where: testing center
EXAM III Quantum mechanics 1. Schrödinger equation in spherical coordinates 2. Hydrogen atom: spherical harmonics 3. Hydrogen atom: radial function and energy 4. Electron’s spin and Pauli matrices 5. Spin and Magnetic field, Combination of two spins
Quantum mechanics Schrödinger equation in spherical coordinates
Quantum mechanics Schrödinger equation in spherical coordinates The angular equation The radial equation x y z r
Quantum mechanics The hydrogen atom Quantization of the energy Bohr radius
Quantum mechanics The hydrogen atom Energies levels Spectroscopy Energy transition Rydberg constant E 0 E1E1 E2E2 E3E3 E4E4 Lyman Balmer Paschen
Quantum mechanics x y z r Normalization Radial part angular part
Quantum mechanics The angular momentum eigenvectors x y z r Spherical harmonics are the eigenfunctions
Quantum mechanics The spin
Quantum mechanics Pauli matrices
Quantum mechanics Adding spins S Possible values for S when adding spins S 1 and S 2 : Clebsch- Gordan coefficients
EXAM II Quantum mechanics Some of the formulae provided Schrödinger equation Potential in hydrogen atom: and Bohr radius: Normalization Angular momentum
Quantum mechanics