Constants, Units, and Conventions

This subgroup is the searchable reference-layer continuation of the Learn convention pages. Use it when a formula looks different across sources and you need to translate constants, unit systems, signs, phases, or matrix conventions.

Main Routes

• SI Units
• Natural Units
• Atomic Units
• Hbar Conventions
• Charge Sign Conventions
• Fourier Convention Translator
• Angular Momentum Convention Translator
• Density Matrix Convention Translator

Default Policy

The default teaching convention keeps $\hbar$ explicit and keeps $c$ explicit unless a page declares otherwise. The elementary charge symbol $e$ is positive; the electron charge is $q_e=-e$. Fourier transforms use symmetric $(2\pi\hbar)^{-1/2}$ factors in one dimension for position-momentum transforms.

For numerical values, use Constants and Units. For conceptual explanation, use Units and Constants.

Translation Checklist

Before comparing two formulas, check:

• which constants are set to one;
• whether energy, frequency, and temperature are being identified;
• whether $e$ means charge magnitude or electron charge;
• whether Fourier variables are $p$ or $k$;
• whether angular momentum states use the same phase convention;
• whether density matrices are abstract operators or basis matrices;
• whether tensor-product order is fixed.

References

• D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018.
• 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.