# Pre-quantum

Blackbody radiation photoelectric effect - photons bohr atom

de broglie waves wave particle dualtiy born nterpretation

# Vectors

quantum statics observations. Hermitian operators eigenvalues

Amplitudes Square = probability

## Qubit / Spin

stern gerlach pauli maatrices

https://x.com/vm_braindumps/status/1042658911491375105?s=20 https://arxiv.org/abs/1809.07287 A Physical Perspective on Control Points and Polar Forms: Bézier Curves, Angular Momentum and Harmonic Oscillators

# Schroedinger Eq

Dirac vs Schroedinger vs Heisenberg $H = i \hbar \partial_t$

Propagators Baker–Campbell–Hausdorff formula Lie Algebra Lie Group https://en.wikipedia.org/wiki/C*-algebra Kac Moody Algebra https://en.wikipedia.org/wiki/Kac%E2%80%93Moody_algebra

## Hydrogen

Spherical Harmonics

Bloch theorem

# Perturbation

WKB variational methods - Helium

Wigner Eckart

# Path Integrals

Gaussian Integrals Hubbard-Stratonovich Fermionic path integral - Grassman numbers

# Scattering

1-d scattering Born Scattering Optical Theorem Fermi’s golden rule

# Many Body and QFT

https://en.wikipedia.org/wiki/Quantum_field_theory

Annihilation and creation operators

Hartree Fock RPA random phase approximation plasmons Bogoliubov Transformations

Gauge theories - ghosts. wilson loops Time Ordering Dyson Equation Wick Contraction Wick Rotation i epsilon keldysh regularization renormalization effective field theory Green’s functions Many body thermo - kadanoff baym Legendre transformation - Effective action, potential Ward Identities

coherent states glauber

particle physics nuclear physics - Blatt and Wiesskopf. Many Body Fetter AMO goofball string theory supersymmttry conformal field theory https://en.wikipedia.org/wiki/Conformal_field_theory OPE operator product expansion bulk bundary correspondence

## Feynman diagrams

1-D Feynman diagrams for SHO perturbaton theory. 0-D Graph summation. Symmetries and isomorphism

import networkx as nx



# Numerical

• Quantum Monte Carlo
• Density Functional Theory
• Density Matrix Renormalization Group
• Exact Diagonalization
• Tensor Networks Matrix Product States

# Foundations

## Quantum information

Bell’s inequality Entanglement

density matrix obervables measurement

Nielson Chang

Grover Shor

# Resources

Griffiths Shankar Ziman - advanced quantum mechanics Sakurai Landau Lishitz Schiff Quantum and Path Integral - Feynman Cogen Tanoudji Weinberg

Ryder Zee Peskin Schroeder Srednicki Tong