Named Models
Named models are reusable idealizations. A model name usually specifies a Hamiltonian family plus assumptions about degrees of freedom, couplings, boundary conditions, and approximation regime. It does not automatically specify units, signs, dimensionality, or all physical corrections.
Entries
Section titled “Entries”| Entry | Compact Role | Canonical Route |
|---|---|---|
| Harmonic Oscillator | Quadratic confinement, ladder structure, zero-point energy, and local normal-mode physics. | Quantum Harmonic Oscillator |
| Hydrogen Atom | Coulomb two-body bound-state problem reduced to a central-potential model. | Hydrogen Atom |
| Jaynes–Cummings Model | Two-level system coupled to a single quantized mode under rotating-wave assumptions. | Interactions and Coupling Terms |
| Hubbard Model | Lattice hopping plus local interaction, central to correlated many-body physics. | Many-Particle Hamiltonians |
Model-Card Questions
Section titled “Model-Card Questions”For any named model, ask:
- What is the Hilbert space?
- What are the degrees of freedom and labels?
- Which Hamiltonian terms are included?
- Which approximations are being made?
- What is exact, perturbative, numerical, or phenomenological?
These questions prevent a model name from becoming a vague citation substitute.
References
Section titled “References”- R. Shankar, Principles of Quantum Mechanics, 2nd ed., Springer, 1994.
- J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.
- A. Altland and B. Simons, Condensed Matter Field Theory, 2nd ed., Cambridge University Press, 2010.
- M. O. Scully and M. S. Zubairy, Quantum Optics, Cambridge University Press, 1997.