Quantum Physics

Foundational quantum mechanics — distinct from the Quantum Chemistry section, which focuses on many-electron Hamiltonians and electronic-structure methods. This section covers the building blocks: single-particle Schrödinger equation, ladder operators, two-level systems, scattering, time evolution, semiclassics, and tools for thinking about quantum systems before the many-body machinery gets invoked.

Planned

• The Schrödinger equation in 1D — bound states, scattering, boundary conditions, basis-set discretizations.
• Harmonic oscillator, algebraically — ladder operators, number states, coherent and squeezed states.
• Angular momentum and spherical harmonics — SU(2) representations, Clebsch-Gordan coefficients.
• Time evolution — Schrödinger vs Heisenberg vs interaction picture; propagator construction; Trotter splitting.
• Spin and two-level systems — Pauli algebra, Bloch sphere, Rabi oscillations.
• WKB and semiclassics — see also the perturbation-methods section.
• Scattering theory — partial waves, Born approximation, T-matrix, S-matrix.
• Density matrices and open systems — reduced density matrix, partial trace, Lindblad master equation, decoherence.

Existing related pages

Until those pages exist here, the QM-flavored material is currently scattered across the chemistry section:

• Harmonic Oscillator (Finite Difference)
• Infinite Square Well
• The Variational Principle
• Real-space vs Second Quantization
• Perturbation Theory, Divergent Series, and Resurgence