This article summarizes equations in the theory of quantum mechanics.
Wavefunctions A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. A common abbreviation is ħ = h/2π, also known as the reduced Planck constant or Dirac constant.
The general form of wavefunction for a system of particles, each with position ri and z-component of spin sz i. Sums are over the discrete variable sz, integrals over continuous positions r. For clarity and brevity, the coordinates are collected into tuples, the indices label the particles (which cannot be done physically, but is mathematically necessary). Following are general mathematical results, used in calculations.
Equations
Wave–particle duality and time evolution
Non-relativistic time-independent Schrödinger equation Summarized below are the various forms the Hamiltonian takes, with the corresponding Schrödinger equations and forms of wavefunction solutions. Notice in the case of one spatial dimension, for one particle, the partial derivative reduces to an ordinary derivative.
Non-relativistic time-dependent Schrödinger equation Again, summarized below are the various forms the Hamiltonian takes, with the corresponding Schrödinger equations and forms of solutions.
Photoemission
Quantum uncertainty
Angular momentum
Magnetic moments
In what follows, B is an applied external magnetic field and the quantum numbers above are used.
Hydrogen atom
See also Defining equation (physical chemistry) List of electromagnetism equations List of equations in classical mechanics List of equations in fluid mechanics List of equations in gravitation List of equations in nuclear and particle physics List of equations in wave theory List of photonics equations List of relativistic equations
Footnotes
Sources P.M. Whelan; M.J. Hodgeson (1978). Essential Principles of Physics (2nd ed.). John Murray. ISBN 0-7195-3382-1. G. Woan (2010). The Cambridge Handbook of Physics Formulas. Cambridge University Press. ISBN 978-0-521-57507-2. A. Halpern (1988). 3000 Solved Problems in Physics, Schaum Series. Mc Graw Hill. ISBN 978-0-07-025734-4. R. G. Lerner; G. L. Trigg (2005). Encyclopaedia of Physics (2nd ed.). VHC Publishers, Hans Warlimont, Springer. pp. 12–13. ISBN 978-0-07-025734-4. C. B. Parker (1994). McGraw Hill Encyclopaedia of Physics (2nd ed.). McGraw Hill. ISBN 0-07-051400-3. P. A. Tipler; G. Mosca (2008). Physics for Scientists and Engineers: With Modern Physics (6th ed.). W. H. Freeman and Co. ISBN 978-1-4292-0265-7. L.N. Hand; J. D. Finch (2008). Analytical Mechanics. Cambridge University Press. ISBN 978-0-521-57572-0. T. B. Arkill; C. J. Millar (1974). Mechanics, Vibrations and Waves. John Murray. ISBN 0-7195-2882-8. H.J. Pain (1983). The Physics of Vibrations and Waves (3rd ed.). John Wiley & Sons. ISBN 0-471-90182-2. J. R. Forshaw; A. G. Smith (2009). Dynamics and Relativity. Wiley. ISBN 978-0-470-01460-8. G. A. G. Bennet (1974). Electricity and Modern Physics (2nd ed.). Edward Arnold (UK). ISBN 0-7131-2459-8. I. S. Grant; W. R. Phillips; Manchester Physics (2008). Electromagnetism (2nd ed.). John Wiley & Sons. ISBN 978-0-471-92712-9. D.J. Griffiths (2007). Introduction to Electrodynamics (3rd ed.). Pearson Education, Dorling Kindersley. ISBN 978-81-7758-293-2.
Further reading L. H. Greenberg (1978). Physics with Modern Applications. Holt-Saunders International W. B. Saunders and Co. ISBN 0-7216-4247-0. J. B. Marion; W. F. Hornyak (1984). Principles of Physics. Holt-Saunders International Saunders College. ISBN 4-8337-0195-2. A. Beiser (1987). Concepts of Modern Physics (4th ed.). McGraw-Hill (International). ISBN 0-07-100144-1. H. D. Young; R. A. Freedman (2008). University Physics – With Modern Physics (12th ed.). Addison-Wesley (Pearson International). ISBN 978-0-321-50130-1.