Learning Objectives

Know, understand, and Use Key Equations

  1. Time-dependent Schrödinger equation.

  2. Time-independent Schrödinger equation

  3. Fermi’s golden rule

  4. Time-correlation formulation for spectral broadening (advanced)

Understand and Apply Key Concepts and Notation

  1. Bra-ket notation.

  2. Hermitian operators

  3. Eigenfunctions/eigenvalues

  4. Expansion in a complete orthonormal set

  5. Dirac delta function

  6. Commutators/Simultaneous observables

  7. Heisenberg Uncertainty Principle

  8. De Broglie wavelength

  9. Planck’s law

  10. “Fundamental experiments” of quantum mechanics like blackbody radiation and the photoelectric effect.

  11. Expectation values and how to evaluate them

  12. Probabilistic interpretation of the wavefunction

  13. Spatial and Spin Orbitals

  14. Slater determinants

  15. Allowable and non-allowable wavefunctions.

  16. Allowable and non-allowable operators.

Know the Ground-state Wavefunctions, Eigenenergies, Quantum Numbers, and Selection Rules for Important Exactly-Solvable Models, and Use Them to Model Real Atomic and Molecular Systems

  1. Particle-in-a-box.

  2. Harmonic Oscillator

  3. Rigid Rotor

  4. One-electron atom

  5. Angular momentum (L, S, J, etc.)

Know, Understand, and Apply Quantum Concepts for Atoms & Molecules

  1. Concept of effective nuclear charge.

  2. Hartree-Fock

  3. Molecular orbital theory; linear combination of atomic orbitals

  4. Valence bond theory.

  5. Term Symbols

  6. Hund’s Rules

  7. Born-Oppenheimer Approximation

  8. Spectroscopy and Selection Rules

Know, Understand, and Apply Approximate Computational Strategies and Associated Practical Computational Methods

  1. Perturbation Theory

  2. Variational Principle

  3. Evaluating expectation values approximately

  4. Slater Determinants and Hartree-Fock

  5. Electron correlation and Correlated Electronic Structure Methods (advanced)