How to Use References

References are tools, not decorations. Use them to check assumptions, compare conventions, deepen explanations, verify claims, and find the right level of detail.

The goal is not to read every cited source. The goal is to know what kind of source you need for the question you have.

Match the Source to the Task

Task	Best source type
First explanation	Introductory textbook or orientation page
Standard derivation	Textbook, lecture notes, or canonical concept page
Convention check	Convention page, formula card, or source with explicit notation
Rigorous hypothesis	Mathematical physics text or theorem page
Historical priority	Original paper plus modern historical commentary
Research status	Review article, monograph, or recent primary literature
Numerical method	Numerical analysis reference plus reproducible benchmark
Formula lookup	Reference entry plus canonical-home link

Use Reference for compact lookup and Bibliography for curated reading routes.

Read Citations Around the Claim

When a page cites a source, ask what the citation supports:

• a definition;
• a standard derivation;
• an experimental result;
• a theorem;
• a convention;
• an approximation method;
• a historical statement;
• a research-frontier claim.

A citation to a textbook is appropriate for standard formalism. A frontier claim usually needs a review or primary research source. A convention dispute needs sources that state conventions explicitly.

For policy, see Citation Standards.

Compare Conventions Before Comparing Formulas

Many apparent disagreements are convention differences:

• Fourier transform signs and factors of $2\pi$;
• $\hbar=1$ versus explicit $\hbar$;
• metric signatures in relativistic formulas;
• spherical-harmonic phases;
• tensor-product ordering;
• active versus passive transformations;
• density-matrix and trace conventions.

Before deciding that two formulas conflict, translate conventions. Start with Conventions Overview.

Use Textbooks by Strength

No textbook is best at everything. A useful reading stack often combines:

• a first-pass textbook for examples and intuition;
• a graduate text for formal structure;
• a specialized monograph for depth;
• a mathematical text for hypotheses and rigor;
• review articles for research areas.

When two sources differ, ask whether they are using different assumptions, notation, approximation regimes, or pedagogical goals.

Use Primary Papers Carefully

Primary papers are essential for original results and research claims, but they are not always the best first explanation. Older papers may use obsolete notation, partial frameworks, or premodern terminology. Recent papers may assume extensive background and may not have been fully absorbed into the standard literature.

Use primary papers when you need:

• historical origin;
• exact theorem statement;
• experimental details;
• research-level nuance;
• a result not yet covered well in textbooks.

Then compare with a review or monograph when possible.

Use Reference Pages for Lookup, Not Full Learning

A reference entry should be compact. It may tell you a formula, symbol, convention, model, or canonical home. It should not be expected to replace a full derivation.

Good use:

1. Look up a formula or symbol in Reference.
2. Check assumptions and convention notes.
3. Follow the canonical-home link if you need the derivation.
4. Return to the reference entry for quick recall later.

Bad use: copying a formula from a table without checking whether the problem satisfies its assumptions.

Build a Personal Source Ladder

For a topic you care about, build a ladder:

Rung	Purpose
Orientation page	What is the topic and why it matters?
Concept page	What is the canonical explanation?
Worked example	How is it used?
Reference entry	What is the compact formula or notation?
Textbook chapter	What is the sustained pedagogical treatment?
Review or monograph	What is the broader domain context?
Primary paper	What was originally proved, measured, or proposed?

You do not need every rung for every topic. The ladder prevents you from asking a quick lookup page to do the work of a monograph.

Common Mistakes

• Treating citations as authority tokens rather than support for specific claims.
• Comparing formulas before comparing conventions.
• Reading primary papers before learning standard notation.
• Treating one favorite textbook as the only valid presentation.
• Using a formula entry without following its assumptions.
• Ignoring review dates and page status.

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.
• L. E. Ballentine, Quantum Mechanics: A Modern Development, 2nd ed., World Scientific, 2014.
• B. C. Hall, Quantum Theory for Mathematicians, Springer, 2013.
• Committee on Publication Ethics, Core Practices, for general correction and citation-integrity principles.

Exercises

1. Two textbooks give different Fourier-transform normalizations. What should you do before deciding one is wrong?

Solution

Check each book’s Fourier convention: signs in the exponent and factors of $2\pi$ in the forward and inverse transforms. Translate one convention into the other before comparing formulas.

2. A page cites a recent paper for a frontier claim. What additional source would often help?

Solution

A review article or monograph can place the result in context, explain assumptions, and indicate whether the claim is broadly accepted, actively debated, or limited to a specialized regime.