G25.2666: Quantum Chemistry and Dynamics Last updated Sep 10, 2020 Save as PDF G25.2651: Statistical Mechanics II 0: The Fundamental Postulates of Quantum Mechanics Page ID20847 Mark E. TuckermanNew York University ( \newcommand{\kernel}{\mathrm{null}\,}\) Topic hierarchy0: The Fundamental Postulates of Quantum Mechanics0.1: The physical state of a quantum system0.2: Physical Observables0.3: Measurement0.4: Time evolution of the state vector0.5: The Heisenberg uncertainty principle0.6: The Heisenberg picture1: The simplest chemical bond: The \(H_2^+\) Ion1.0: Variational Theory and the Variational Principle1.1: Example 1: The Harmonic Oscillator1.2: Example 2: The Harmonic Oscillator Revisited1.4: An example of the variational theory: The \(H_2^+\) molecule ion1.4a: The trial wavefunction: a linear combination of atomic orbitals1.4b: Bonding and anti-bonding orbitals1.4c: Improvements on the approximation1.4D: Other Molecular Orbitals2: General theory of spin2.0: Experimental evidence for electron spin2.1: Fine structure of spectral lines2.2: Anomalous Zeeman effect2.3: Evidence for half-integer Angular Momentum2.4: The Uhlenbeck and Goudsmit proposal2.1: Representing states in the full Hilbert space2.3: Rotations in spin space2.4: Some group theoretic concepts2.5: Explicit form of the spin-1/2 rotation operator2.5: Introduction to the Dirac Equation2.7: Solution of the Dirac equation for a free particle3: Systems of Identical Particles4: Molecular Quantum Mechanics4.2: Total orbital angular momentum4.3: A simple example of angular momentum addition4.3: Total spin4.7: The general problem4.8: The simple example revisited4.9: Final remarks5: Time-dependent Perturbation Theory6: Interactions with an electromagnetic field: Spectroscopy7: Scattering Theory8: The Feynman Path Integral Formulation Contributors and Attributions Mark Tuckerman (New York University)