What This Site Is

This project is a long-term, graduate-level reference for quantum mechanics. It is designed to serve six connected roles:

1. a living encyclopedia;
2. a guided curriculum;
3. a research atlas;
4. a computational laboratory;
5. a reference library;
6. a bridge to quantum field theory.

Those roles share one editorial objective: make correct statements, assumptions, derivations, conventions, limitations, and sources easier to find and maintain. Page count is not the measure of success. A useful reference reduces ambiguity and helps a reader move from orientation to a canonical explanation, then from that explanation to applications and primary literature.

Who It Is For

The primary audience is graduate students and researchers who need more than a one-semester narrative. The pages also support:

• first-time learners seeking a dependency-aware route;
• undergraduates consolidating a course;
• graduate students preparing for qualifying examinations;
• researchers refreshing a neighboring subfield;
• mathematical readers checking analytic assumptions;
• computational readers validating an algorithm or benchmark;
• readers moving between quantum mechanics and quantum field theory.

Accessibility does not mean removing the mathematics. It means introducing notation, motivation, assumptions, and physical interpretation before relying on them.

Use Choose Your Path to select a route by background and goal. Use Levels and Audience to interpret page-level difficulty labels.

A Living Encyclopedia

The encyclopedia role gives each major topic one canonical home. That page owns the durable definition, principal derivation, assumptions, and standard interpretation. Other pages can preview, apply, summarize, or reference the topic, but they should link to the canonical page instead of reproducing its full argument.

This rule matters because duplicated derivations drift. A sign correction, convention change, or stronger hypothesis can be fixed reliably when one page owns the result. Cross-links then carry that correction throughout the subject.

A canonical page is expected to improve over time. Its status may move from draft to reviewed or mature as technical checks, references, examples, and expert review accumulate. Versioning and Review Policy defines that lifecycle.

A Guided Curriculum

The curriculum role prevents readers from being abandoned inside a large index. Roadmaps provide paths for:

• a first quantum-mechanics course;
• undergraduate and graduate physics;
• mathematical quantum mechanics;
• computational quantum mechanics;
• quantum information;
• atomic, molecular, and optical physics;
• chemistry and molecular science;
• condensed-matter physics;
• research refreshers;
• preparation for field theory.

These paths are not rigid schedules. They are dependency-aware routes through a network. A reader can skip material already known, follow one prerequisite when blocked, and return to the main route.

The Roadmaps chapter owns those paths. The Prerequisites chapter supplies diagnostic checklists, and the Study System chapter supplies workflows for reading derivations, solving problems, and using references.

A Research Atlas

The atlas role shows where one concept reappears across physics without duplicating its canonical treatment.

A density operator belongs to Core Formalism, but reduced states and entropy also appear in quantum information, open systems, many-body physics, statistical mechanics, and foundations. The harmonic oscillator is a canonical system, but it also models vibrations, photons, phonons, circuit modes, normal modes, and local approximations near stable equilibria.

An atlas-quality page should distinguish:

• the canonical definition from an application;
• a theorem from a convention;
• an exact result from an approximation;
• a standard approximation from a regime-specific heuristic;
• settled knowledge from an active research claim.

The Map of Quantum Mechanics and How the Volumes Fit Together provide the high-level map. Individual pages provide the local cross-links.

A Computational Laboratory

Many quantum problems are understood only after analytic reasoning and computation meet. The computational role connects conceptual pages to:

• reproducible notebooks;
• benchmark spectra and wavefunctions;
• convergence and truncation checks;
• dimensional and limiting-case tests;
• numerical error estimates;
• algorithm assumptions and failure modes;
• reproducible figure sources.

A plot is not evidence by itself. A computational result should state the model, units, discretization, boundary conditions, solver, tolerances, convergence test, and comparison target when those details affect the claim.

Use the Computational Quantum Mechanics Roadmap for a study path and How to Use Notebooks for the expected validation workflow.

A Reference

The Reference is the compact lookup layer. It contains definitions, symbols, formulas, theorem statements, model cards, experiment cards, derivation indexes, problem indexes, and bibliographic guides.

Reference entries are intentionally denser and shorter than canonical concept pages. They should:

• state assumptions and conventions;
• identify the exact object being defined or quoted;
• link to a canonical derivation;
• avoid silently changing notation;
• cite a suitable source;
• remain useful without duplicating an entire chapter.

Use a reference entry when recalling a result. Use the linked canonical page when learning, deriving, or checking its scope.

A Bridge to Field Theory

Quantum mechanics owns fixed-particle nonrelativistic states, wavefunctions, spin, density matrices, entanglement basics, standard nonrelativistic scattering, and the harmonic oscillator as a canonical system.

Quantum field theory owns relativistic quantum fields, field quantization, particle creation and annihilation as structural features, renormalization, and gauge-field dynamics. The two frameworks share Hilbert spaces, operators, amplitudes, symmetry, and measurement language, but they are not interchangeable.

Bridge pages should explain both continuity and boundary. They should not force field-theoretic machinery into a nonrelativistic page merely because a later application uses it. Relationship to the QFT Site owns the detailed split and reading route.

The Canonical-Home Rule

Every recurring topic should have:

• one canonical concept or derivation page;
• compact reference entries where lookup is useful;
• application pages that import the result;
• cross-links that make ownership explicit.

For example, an application may state the uncertainty relation it uses and link to its canonical derivation. It should not repeat the full proof unless a new assumption or specialized variant is genuinely part of the application.

Canonical ownership does not forbid repetition of a definition or essential formula. It prevents multiple pages from claiming independent ownership of the same full explanation.

Promise for Mature Pages

A mature concept page should normally contain:

Element	Reader promise
Purpose or definition	The page states what object, result, or question it owns
Motivation	The reader can see why the topic matters
Prerequisites and conventions	Hidden assumptions are made visible
Mathematical formulation	Symbols, domains, and hypotheses are stated
Physical interpretation	Formal expressions are connected to predictions
Worked examples	At least one nontrivial use is shown where appropriate
Limitations and common mistakes	The page marks where the result fails or is overread
References	Claims can be traced to authoritative sources
Exercises	Readers can test understanding when exercises suit the page type
Cross-links	Prerequisites, applications, and canonical ownership are navigable

Not every page has the same shape. A glossary entry, convention page, theorem card, roadmap, or editorial policy may be shorter and may not need exercises. It still needs a clear purpose, scope, source trail, and canonical links.

Evidence and Knowledge Status

Claims should be labeled by what is known, not by how exciting they sound. The editorial layer distinguishes:

• standard textbook results;
• rigorous theorems under stated assumptions;
• controlled approximations;
• experimentally established findings;
• active research;
• conjecture or speculation.

Frontier pages should identify uncertainty, competing explanations, and open questions. Technology pages should distinguish laboratory demonstrations from scalable systems and commercial readiness.

Evidence Labels defines the categories. Citation Standards defines when primary, review, textbook, or reference sources are appropriate.

Reproducibility and Correction

Trust is maintained through visible process:

1. important claims cite appropriate sources;
2. derivations expose assumptions and conventions;
3. figures retain source files when practical;
4. numerical work reports validation checks;
5. internal links identify canonical ownership;
6. pages carry review and knowledge-status metadata;
7. errors are corrected rather than hidden.

Found a mathematical error, unsupported claim, ambiguous convention, broken link, or inaccessible figure? Use Report Errors and include the page, location, expected correction, and supporting evidence when available.

Contributions should improve the canonical structure rather than create a parallel version of the same topic. Contribute describes the expected scope and review information.

What It Is Not

This project is not a replacement for instructors, primary literature, laboratory training, or sustained problem solving. It is not a feed of unfiltered quantum news, a catalogue of unexplained “weirdness,” or a venue where speculative claims are presented as established theory.

What This Site Is Not is the canonical page for those boundaries.

References

• P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed., Oxford University Press (1958).
• 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).
• M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010).
• B. C. Hall, Quantum Theory for Mathematicians, Springer (2013).
• M. H. Kalos and P. A. Whitlock, Monte Carlo Methods, 2nd ed., Wiley-VCH (2008).