The two-semester sequence, ASTR 5110 and 5120, provides an introduction to the "Physics of Astrophysics" for first-year graduate students in APS. In the first semester, we cover aspects of applied quantum mechanics, spectroscopy, emission/absorption lines, ionization and thermal physics, kinetic theory, and statistical mechanics. The course will include numerous homework sets, which will be returned with solutions. The course grade will be based on: homework (60%), final exam (20%), final project and paper (10%), and the quality and effectiveness of class participation (10%). In class, we will discuss the broader implications of physical processes from the course to recent scientific papers, order-of-magnitude estimation, and oral discussion. The material for the first semester will include aspects of the following topics:

Introduction and Review of Quantum Mechanics:

- Operators, Schroedinger Equation, Angular Momentum
- Relationships to Classical Mechanics (orbits, angular momentum, etc.)
- Perturbation Theory (time-independent, time-dependent)
- Hydrogen atom and its spectroscopy
- Central potentials: wavefunctions and spherical harmonics
- Spin, magnetic moments, fine structure, hyperfine structure, Zeeman effect

Multi-electron spectroscopy:

- Single-electron orbitals (shells, sub-shells)
- Hamiltonian with perturbation terms
- L-S coupling (configurations, terms, levels)
- Isoelectronic sequences and Generalized Pauli Principle
- Angular momentum coupling, "raising & lowering" operators, Clebsch-Gordan coefficients
- Radiative selection rules: allowed, forbidden, semi-forbidden, fine-structure lines

Emission and Absorption Lines, Radiative Transitions, Opacities

- Blackbody spectrum, quantum oscillators (second quantization)
- Two-level atom, Einstein "A and B relations", stimulated emission, maser action
- Absorption and emission processes, optical depth, curve of growth
- Line profile functions (Doppler, Lorentz, Voigt profiles)
- Radiative transfer equation, emissivity and absorption coefficients
- Non-LTE, 2-level atom
- Opacity processes (continuum and lines; radio/IR through UV/X-ray/gamma-ray)

Ionization, Excitation, Radiative Cooling

- Ionization Equilibrium (Coronal, photoionization, Saha models)
- Processes and rate coefficients (collisional ioniz., radiative and dielectronic recombination)
- Collisional excitation/de-excitation and detailed balance
- (2-level atom, collision strengths, line quenching)
- Radiative cooling function and plasma diagnostics (density, temperature, abundances, etc.)
- Thermal equilibrium and thermal instability

Molecular Physics and Spectroscopy

- Molecular orbitals: bonding and anti-bonding, Born-Oppenheimer approx.
- Rigid rotator, harmonic oscillator, and departures
- Electronic, vibrational, and rotational spectra
- Effects of nuclear spin: homonuclear molecules (H2, N2, O2, etc.)
- Nuclear motion, Franck-Condon principle, Lambda-doubling
- Molecule formation, destruction, pre-dissociation

Review of Thermodynamics

- Laws of thermodynamics
- State variables, mathematical theorems, Maxwell relations, Legendre transformations
- Phase diagrams, latent heats, Adiabatic processes, isothermal processes
- Heat transport processes (conduction, radiation, etc.)

Introduction to Statistical Mechanics

- Microstates and macrostates, phase space
- Statistical definitions of temperature, entropy, chemical potential
- Enthalpy, Helmholtz and Gibbs Free Energies
- N-dimensional phase space, entropy of mixing, Gibbs paradox
- Review of Hamiltonian mechanics and phase-space trajectories
- Poincare invariant theorem, Poisson brackets, Liouville's Theorem

Micro-Canonical and Canonical Ensembles

- Phase-space density function and ensemble averages
- Derivation of thermodynamic functions, equipartition theorem
- Boltzmann statistics, partition functions, and applications
- Paramagnetism (classical and quantum versions; spin-1/2 and general spin
- Ideal gases (classical), harmonic oscillator (classical and quantum)
- Thermal equilibrium (Gibbs function, chemical potentials, Saha equation)

Grand Canonical Ensemble

- Grand partition function, fugacity
- Derivation of thermodynamic variables
- Applications: ideal gases, Fermi-Dirac & Bose-Einstein statistics
- Equation of state derived from Grand Partition Function

Quantum Statistics (Fermi-Dirac, Bose-Einstein)

- Derivation of FD and BE statistics from micro-canonical ensemble
- Properties of FD and BE distributions (Fermi level, BE condensation)
- Equations of state (relativistic and non-relativistic ideal gases)
- Photon (BE) and neutrino (FD) statistics
- Critical temperatures and Bose-Einstein phase transitions