Physics:Quantum Formulas Collection



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Formulas Collection this page provides a list of the most important formulas in quantum mechanics, useful as a quick reference for students, teachers, and researchers. The formulas are organized by topic and include names, mathematical expressions, and short explanations of what they mean and how they are used. While this collection focuses on key results, science is always evolving, and new discoveries may override or extend these formulas. You, the reader, are welcome to suggest additions or corrections to keep this resource up to date. This page provides a list of the most important formulas in quantum mechanics, useful as a quick reference for students, teachers, and researchers. This table lists key formulas in quantum mechanics, showing their names, expressions, and applications.

Quantum Formulas Collection.

Key Formulas in Quantum Mechanics

This table lists key formulas in quantum mechanics, showing their names, expressions, and applications.

Equation Name	Formula	Description	Applications
Angular Momentum Components	$L_z=m_{\ell }\hslash$	Z-component of angular momentum.	Quantized orbits.
Compton Effect: Change in Wavelength	$\mathrm{\Delta }\lambda =\frac{h}{m_{e}c}(1-\cos \theta )$	Shift in photon wavelength after scattering.	Compton scattering, evidence for photon momentum.
Cutoff Wavelength	${\lambda }_{min}=\frac{hc}{K_0}$	Minimum wavelength in bremsstrahlung.	X-ray production.
De Broglie Wavelength	$p=\frac{h}{\lambda }=\hslash k$	Wavelength associated with a particle's momentum.	Matter waves, electron diffraction.
Occupancy Probability	$P(E)=\frac{1}{e^{(E-E_F)/kT}+1}$	Fermi-Dirac distribution.	Electron statistics in metals.
Density of States	$N(E)=8\sqrt{2}\pi m^{3/2}{E}^{1/2}/h^3$	Number of states per energy interval (3D free electron gas).	Solid-state physics, Fermi gas.
Dirac Equation	$(\mathit{\beta }m{c}^2+c\sum _{k=1}^3{\mathit{\alpha }}_k{p}_k)\mathrm{\Psi }=i\hslash \frac{\partial }{\partial t}\mathrm{\Psi }$	Relativistic quantum equation for fermions.	Particle physics, electrons.
Electric Dipole Potential Energy	$V=-\mathbf{𝐩}\cdot \mathbf{𝐄}$	Energy of dipole in electric field.	Molecular physics.
Electrostatic, Coulomb Potential Energy	$V=\frac{q_1{q}_2}{4\pi {ϵ}_{0}r}$	Coulomb potential.	Atomic interactions.
Free Particle Schrödinger's Equation (1D)	$-\frac{{\hslash }^2}{2m}\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathrm{\Psi }=E\mathrm{\Psi }$	For free particle in 1D.	Free particle motion.
Free Particle Schrödinger's Equation (3D)	$-\frac{{\hslash }^2}{2m}{\mathrm{\nabla }}^2\mathrm{\Psi }=E\mathrm{\Psi }$	For free particle in 3D.	Scattering problems.
Harmonic Oscillator Potential Energy	$V=\frac{1}{2}k{x}^2$	Potential for harmonic oscillator.	Vibrational modes, quantum optics.
Heisenberg's Uncertainty Principle	$\mathrm{\Delta }x\mathrm{\Delta }{p}_x\ge \frac{\hslash }{2}$ $\mathrm{\Delta }E\mathrm{\Delta }t\ge \frac{\hslash }{2}$	Limits on simultaneous knowledge of position/momentum and energy/time.	Fundamental limit in measurements, quantum tunneling.
Hydrogen Atom, Orbital Energy	$E_n=-\frac{m{e}^4}{8{ϵ}_0^2{h}^2{n}^2}=-\frac{13.6\mathrm{e}\mathrm{V}}{n^2}$	Energy levels of hydrogen atom.	Atomic spectroscopy, Bohr model.
Hydrogen Atom, Radial Probability Density	$P(r)=\frac{4r^2}{a^3}{e}^{-2r/a}$	Probability density for electron position (ground state).	Atomic orbitals.
Hydrogen Atom Spectrum, Rydberg Equation	$\frac{1}{\lambda }=R_H(\frac{1}{n_2^2}-\frac{1}{n_1^2})$	Wavelengths of spectral lines.	Hydrogen emission/absorption spectra.
Infinite Potential Well Energy Levels	$E_n={\left(\frac{hn}{2L}\right)}^2\frac{1}{2m}$	Energy levels for particle in a box.	Quantum confinement, nanostructures.
Klein-Gordon Equation	$(-\frac{1}{c^2}\frac{{\partial }^2}{\partial t^2}+{\mathrm{\nabla }}^2)\mathrm{\Psi }={\left(\frac{m_{0}c}{\hslash }\right)}^2\mathrm{\Psi }$	Relativistic equation for bosons.	Scalar particles.
Law of Probability Conservation for Quantum Mechanics	$\frac{\partial }{\partial t}\underset{V}{\int }|\mathrm{\Psi }{|}^2\mathrm{d}V+\underset{S}{\int }\mathbf{𝐣}\cdot \mathrm{d}\mathbf{𝐀}=0$	Conservation of probability.	Quantum dynamics.
Magnetic Dipole Potential Energy	$V=-\mathbf{𝐦}\cdot \mathbf{𝐁}$	Energy of dipole in magnetic field.	Magnetic resonance.
Moseley's Law	$f=\frac{c}{\lambda }=M_{K_{\alpha }}(Z-1{)}^2$ $M_{K_{\alpha }}=2.47\times 10^{15}$ Hz	Frequency of K-α X-ray line.	Atomic number determination, X-ray spectroscopy.
Normalization Integral	$\underset{\mathbf{𝐫}\in R}{\int }|\mathrm{\Psi }{|}^2\mathrm{d}V=1$	Normalizes the wavefunction.	Probability calculations.
One-Dimensional Box Potential Energy	$V=\{\begin{array}{ll}0& x\in [a,b]\\ \mathrm{\infty }& x\notin [a,b]\end{array}$	Potential for particle in a box.	Quantum wells.
Orbital Electron Magnetic Dipole Components	${\mathit{\mu }}_{orb,z}=-m_{\ell }{\mu }_B$	Z-component of orbital magnetic moment.	Zeeman effect.
Orbital Electron Magnetic Dipole Moment	${\mathit{\mu }}_{orb}=-e\mathbf{𝐋}/2m$	Magnetic moment due to orbital motion.	Atomic magnetism.
Orbital, Electron Magnetic Dipole Moment Potential	$U=-{\mathit{\mu }}_{orb}\cdot {\mathbf{𝐁}}_{ext}=-{\mu }_{orb,z}{B}_{ext}$	Potential in external field.	Magnetic interactions.
Spin, Electron Magnetic Dipole Moment	${\mathit{\mu }}_{\mathbf{𝐬}}=-\frac{e}{m}\mathbf{𝐒}=-g\frac{e}{2m}\mathbf{𝐒}$	Spin magnetic moment.	Electron spin resonance.
Photoelectric Effect: Maximum Kinetic Energy	$E_{\mathrm{k}\mathrm{m}\mathrm{a}\mathrm{x}}=hf-\mathrm{\Phi }$	Maximum kinetic energy of photoelectrons.	Photoelectric effect experiments, solar cells.
Photon Momentum	$p=\frac{hf}{c}=\frac{h}{\lambda }$	Momentum of a photon.	Quantum optics, Compton scattering.
Planck–Einstein Equation	$E=hf=\frac{hc}{\lambda }$	Relates energy of a photon to its frequency or wavelength.	Wave-particle duality, photon energy calculations.
Planck's Radiation Law (Frequency Form)	$I(\nu ,T)=\frac{2h{\nu }^3}{c^2}\frac{1}{e^{\frac{h\nu }{kT}}-1}$	Spectral radiance for blackbody in frequency.	Blackbody radiation, stellar spectra.
Planck's Radiation Law (Wavelength Form)	$I(\lambda ,T)=\frac{2h{c}^2}{{\lambda }^5}\frac{1}{e^{\frac{hc}{\lambda kT}}-1}$	Spectral radiance for blackbody in wavelength.	Thermal radiation analysis.
Probability Current (Non-Relativistic)	$\mathbf{𝐣}=\frac{\hslash }{2mi}({\mathrm{\Psi }}^{*}\mathrm{\nabla }\mathrm{\Psi }-\mathrm{\Psi }\mathrm{\nabla }{\mathrm{\Psi }}^{*})$	Flow of probability.	Current in quantum systems.
Probability Density Function	$\rho (\mathbf{𝐫},t)=|\mathrm{\Psi }(\mathbf{𝐫},t){|}^2$	Probability density.	Locating particles.
Schrödinger's Equation (General Form)	$\hat{H}\mathrm{\Psi }=E\mathrm{\Psi }$	Fundamental equation of quantum mechanics.	Solving quantum systems.
Spin Angular Momentum Magnitude	$S=\hslash \sqrt{s(s+1)}$	Magnitude of spin.	Particle spin properties.
Spin Projection Quantum Number	$m_s\in \{-\frac{1}{2},+\frac{1}{2}\}$	Spin along z-axis for electrons.	Spintronics, NMR.
Time-Dependent Schrödinger's Equation (1D)	$(-\frac{{\hslash }^2}{2m}\frac{{\partial }^2}{\partial x^2}+V)\mathrm{\Psi }=i\hslash \frac{\partial }{\partial t}\mathrm{\Psi }$	Time evolution in 1D.	Dynamics of quantum systems.
Time-Dependent Schrödinger's Equation (3D)	$(-\frac{{\hslash }^2}{2m}{\mathrm{\nabla }}^2+V)\mathrm{\Psi }=i\hslash \frac{\partial }{\partial t}\mathrm{\Psi }$	Time evolution in 3D.	Quantum simulations.
Time-Independent Schrödinger's Equation (1D)	$(-\frac{{\hslash }^2}{2m}\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}+V)\mathrm{\Psi }=E\mathrm{\Psi }$	Stationary states in 1D.	Bound states, potentials.
Time-Independent Schrödinger's Equation (3D)	$(-\frac{{\hslash }^2}{2m}{\mathrm{\nabla }}^2+V)\mathrm{\Psi }=E\mathrm{\Psi }$	Stationary states in 3D.	Atomic and molecular physics.
Wavefunction of a Trapped Particle, One Dimensional Box	${\mathrm{\Psi }}_n(x)=A\sin \left(\frac{n\pi x}{L}\right)$	Wavefunction for particle in a box.	Bound states, quantum wells.
Work Function	$\mathrm{\Phi }=h{f}_0$	Minimum energy to eject an electron.	Photoelectric effect, surface physics.

2. Organized by topic

Below are the same formulas grouped

Quantum mechanics (QM)



Core Dynamical Equations

Time-Dependent Schrödinger Equation $i\hslash ,{\partial }_t\mathrm{\Psi }=\hat{H}\mathrm{\Psi }$

Time-Independent Schrödinger Equation $\hat{H}\psi =E\psi$

Time-Evolution Operator $U(t)=e^{-i\hat{H}t/\hslash }$

Operators and Measurement Theory

Canonical Commutation Relation (Heisenberg) $[x,p]=i\hslash$

Expectation Value $⟨A⟩=⟨\psi |A|\psi ⟩$

Born Rule (Measurement Probability) $P(a)=|⟨a|\psi ⟩{|}^2$

Harmonic Oscillator

Annihilation Operator $a=\frac{1}{\sqrt{2\hslash m\omega }},(m\omega x+ip)$

Energy Levels $E_n=\hslash \omega (n+\frac{1}{2})$

Perturbation Theory & Quantum Transitions

First-Order Energy Correction $E_n^{(1)}=⟨n|V|n⟩$

Fermi Golden Rule (Transition Rate) $\mathrm{\Gamma }=\frac{2\pi }{\hslash },|V_{fi}{|}^2,\rho (E)$

Continuity Equation & Probability Current

Probability Current $j=\frac{\hslash }{2mi}({\psi }^{\mathrm{\nabla }}\psi -\psi \mathrm{\nabla }{\psi }^{)}$

Open quantum systems

• Density Matrix (Statistical Mixture) $\rho =\sum _i{p}_i,|{\psi }_i⟩⟨{\psi }_i|$

• Lindblad Master Equation (Markovian Open Systems) $\dot{\rho }=-\frac{i}{\hslash }[\hat{H},\rho ]+\sum _k{𝒟}[L_k]\rho$

• von Neumann Entropy $S=-\mathrm{T}\mathrm{r}(\rho \log \rho )$

Quantum information science (QIS)

$I(A:B)=S(A)+S(B)-S(AB)$

$\mathrm{\Phi }(\rho )=\sum _k{A}_k\rho A_k^{†}$ (quantum channels)

• Bell states $|{\psi }^{\pm }⟩$, $|{\varphi }^{\pm }⟩$

• CNOT gate definition

• Qubit superposition $|\psi ⟩=\alpha |0⟩+\beta |1⟩$

Quantum optics (QO)

$a,a^{†}$ creation–annihilation operators

$H_{\text{int}}=-\mathbf{𝐝}\cdot \mathbf{𝐄}$

• Coherent state $|\alpha ⟩=e^{-|\alpha {|}^2/2}\sum _n\frac{{\alpha }^n}{\sqrt{n!}}|n⟩$

• Jaynes–Cummings Hamiltonian $H=\hslash \omega a^{†}a+\frac{1}{2}\hslash {\omega }_0{\sigma }_z+g(a^{†}{\sigma }_{-}+a{\sigma }_{+})$

Quantum statistical mechanics

• Partition function $Z=\mathrm{T}\mathrm{r}(e^{-\beta H})$

• Thermal state ${\rho }_{\beta }=e^{-\beta H}/Z$

• Response function $\chi (\omega )$

Quantum field theory (QFT)

• Canonical commutation $[\varphi (x),\pi (y)]=i\hslash \delta (x-y)$

• Klein–Gordon equation $(◻+m^2)\varphi =0$

• Dirac Lagrangian

• Relativistic dispersion $E^2=p^2{c}^2+m^2{c}^4$

3. Multi column version

• $i\hslash {\partial }_t\mathrm{\Psi }=H\mathrm{\Psi }$
• $H\psi =E\psi$
• $\mathrm{\Delta }x\mathrm{\Delta }p\ge \hslash /2$
• $[x,p]=i\hslash$
• $P(a)=|⟨a|\psi ⟩{|}^2$
• $\rho =\sum p_i|{\psi }_i⟩⟨{\psi }_i|$
• $S=-\mathrm{T}\mathrm{r}(\rho \log \rho )$
• $E_n=\hslash \omega (n+1/2)$
• $a=(m\omega x+ip)/\sqrt{2\hslash m\omega }$
• $\mathrm{\Gamma }=\frac{2\pi }{\hslash }|V_{fi}{|}^2\rho (E)$
• $I(A:B)=S(A)+S(B)-S(AB)$
• Bell states $|{\psi }^{\pm }⟩$
• CNOT $=|0⟩⟨0|\otimes I+|1⟩⟨1|\otimes X$
• $\dot{\rho }=-\frac{i}{\hslash }[H,\rho ]+\sum {𝒟}[L]\rho$
• $[\varphi (x),\pi (y)]=i\hslash \delta (x-y)$
• $(◻+m^2)\varphi =0$
• $Z=\mathrm{T}\mathrm{r}(e^{-\beta H})$

4. Wave Packet spreading example

Free particle dispersion: ${\sigma }_x(t)={\sigma }_x(0)\sqrt{1+{\left(\frac{\hslash t}{2m{\sigma }_x(0{)}^2}\right)}^2}$ → Used in cold-atom clouds, ultrafast electron microscopy.

Two-level Rabi oscillation

Population oscillation: $P_e(t)={\sin }^2(\mathrm{\Omega }t/2)$ → Atomic clocks, qubit control.

Harmonic oscillator example

Ground state energy: $E_0=\frac{1}{2}\hslash \omega$ → Zero-point fluctuations in quantum optics.

Formula	Description	Applications
$i\hslash \frac{\partial }{\partial t}\mathrm{\Psi }=\hat{H}\mathrm{\Psi }$	Time-dependent Schrödinger equation	Dynamics, atoms, molecules
$\hat{H}\psi =E\psi$	Time-independent Schrödinger equation	Spectra, tunneling, bound states
$\mathrm{\Delta }x\mathrm{\Delta }p\ge \frac{\hslash }{2}$	Heisenberg uncertainty	Measurement limits, wave packets
$[x,p]=i\hslash$	Canonical commutator	Quantization, oscillators
$⟨A⟩=⟨\psi |A|\psi ⟩$	Expectation value	Predictions, statistics
$P(a)=|⟨a|\psi ⟩{|}^2$	Born rule	Measurement probabilities
$\hat{U}(t)=e^{-iHt/\hslash }$	Time-evolution operator	Quantum gates, scattering
$\rho =\sum _i{p}_i|{\psi }_i⟩⟨{\psi }_i|$	Density matrix	Decoherence, open systems
$S=-\mathrm{T}\mathrm{r}(\rho \log \rho )$	von Neumann entropy	Entanglement, thermodynamics
$\mathrm{T}\mathrm{r}(\rho A)$	Expectation via density matrix	Ensembles, thermal states
$\frac{d\rho }{dt}=-\frac{i}{\hslash }[H,\rho ]+\sum _k{𝒟}[L_k]\rho$	Lindblad master eq.	Decoherence, dissipation
${𝒟}[L]\rho =L\rho L^{†}-\frac{1}{2}\{L^{†}L,\rho \}$	Dissipator	Relaxation, noise
$Z=\mathrm{T}\mathrm{r}(e^{-\beta H})$	Partition function	Thermodynamics, blackbody
$\psi (x)=\frac{1}{\sqrt{2\pi \hslash }}\int dp{e}^{ipx/\hslash }\varphi (p)$	Fourier relation	Wavepackets, scattering
$j=\frac{\hslash }{2mi}({\psi }^{*}\mathrm{\nabla }\psi -\psi \mathrm{\nabla }{\psi }^{*})$	Probability current	Continuity, tunneling
$\hat{a}=\frac{1}{\sqrt{2\hslash m\omega }}(m\omega x+ip)$	Annihilation operator	QHO, quantum optics
$E_n=\hslash \omega (n+\frac{1}{2})$	HO spectrum	Phonons, cavities
${\varphi }_n(x)=\dots$	HO eigenfunctions	Basis for perturbation theory
${\hat{H}}_{\text{spin}}=-\gamma \mathbf{𝐁}\cdot \mathbf{𝐒}$	Spin Hamiltonian	NMR, ESR, qubits
$\chi (\omega )=\underset{0}{\overset{\mathrm{\infty }}{\int }}dt{e}^{i\omega t}C(t)$	Response function	Conductivity, noise
$k=\sqrt{2mE}/\hslash$	Free-particle wavenumber	Beams, dispersion
$\psi (x)=\sum _n{c}_n{\varphi }_n(x)$	Basis expansion	Computation, spectral theory
$H=H_0+\lambda V$	Perturbation theory split	Approximations, resonances
$E_n^{(1)}=⟨n|V|n⟩$	1st-order energy shift	Stark, Zeeman effects
$\mathrm{\Gamma }=\frac{2\pi }{\hslash }|⟨f|V|i⟩{|}^2\rho (E_f)$	Fermi golden rule	Transition rates
$(a|b)=\mathrm{T}\mathrm{r}(a^{†}b)$	Hilbert-Schmidt inner product	Superoperators, channels
$\mathrm{\Phi }(\rho )=\sum _k{A}_k\rho A_k^{†}$	CPTP map (quantum channel)	Noise, quantum info
$I(A:B)=S(A)+S(B)-S(AB)$	Mutual information	Correlations, QIT
$|{\psi }^{\pm }⟩=\frac{1}{\sqrt{2}}(|01⟩\pm |10⟩)$	Bell states	Entanglement, teleportation
$U_{\text{CNOT}}=|0⟩⟨0|\otimes I+|1⟩⟨1|\otimes X$	CNOT gate	Quantum computing
$[\varphi (x),\pi (y)]=i\hslash \delta (x-y)$	Canonical QFT commutator	Field quantization
$E^2=p^2{c}^2+m^2{c}^4$	Relativistic dispersion	QFT, particles
${ℒ}=\overline{\psi }(i{\gamma }^{\mu }{\partial }_{\mu }-m)\psi$	Dirac Lagrangian	Fermions, QED
$◻\varphi +m^2\varphi =0$	Klein-Gordon eq.	Bosons, relativistic waves

Index

Core theory

1. Foundations

2. Conceptual and interpretations

3. Mathematical structure and systems

4. Atomic and spectroscopy

5. Wavefunctions and modes

6. Quantum dynamics and evolution

7. Measurement and information

8. Quantum information and computing

Applications and extensions

9. Quantum optics and experiments

10. Open quantum systems

11. Quantum field theory

12. Statistical mechanics and kinetic theory

13. Condensed matter and solid-state physics

14. Plasma and fusion physics

15. Timeline

16. Advanced and frontier topics

Book II

• Matter by scale

Book III

• Methods and tools

Book IV

• Data Analysis Techniques

Full contents

1. Foundations (14) Back to index

1. Physics:Quantum basics

2. Physics:Quantum photoelectric effect

3. Physics:Quantum black-body radiation

4. Physics:Quantum Planck constant

5. Physics:Quantum Postulates

6. Physics:Quantum Hilbert space

7. Physics:Quantum Observables and operators

8. Physics:Quantum mechanics

9. Physics:Quantum mechanics measurements

10. Physics:Quantum state

11. Physics:Quantum system

12. Physics:Quantum superposition

13. Physics:Quantum probability

14. Physics:Quantum Mathematical Foundations of Quantum Theory

2. Conceptual and interpretations (14) Back to index

15. Physics:Quantum Interpretations of quantum mechanics

16. Physics:Quantum Wave–particle duality

17. Physics:Quantum Complementarity principle

18. Physics:Quantum Uncertainty principle

19. Physics:Quantum Measurement problem

20. Physics:Quantum Bell's theorem

21. Physics:Quantum Hidden variable theory

22. Physics:Quantum nonlocality

23. Physics:Quantum contextuality

24. Physics:Quantum Darwinism

25. Physics:Quantum A Spooky Action at a Distance

26. Physics:Quantum A Walk Through the Universe

27. Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together

28. Physics:Quantum measurement problem

3. Mathematical structure and systems (15) Back to index

29. Physics:Quantum Density matrix

30. Physics:Quantum Exactly solvable quantum systems

31. Physics:Quantum many-body problem

32. Physics:Quantum Formulas Collection

33. Physics:Quantum A Matter Of Size

34. Physics:Quantum Symmetry in quantum mechanics

35. Physics:Quantum Noether theorem

36. Physics:Quantum Angular momentum operator

37. Physics:Quantum Runge–Lenz vector

38. Physics:Quantum Approximation Methods

39. Physics:Quantum Matter Elements and Particles

40. Physics:Quantum Dirac equation

41. Physics:Quantum Klein–Gordon equation

42. Physics:Quantum pendulum

43. Physics:Quantum configuration space

4. Atomic and spectroscopy (14) Back to index

Quantum atomic structure and spectroscopy: orbitals, energy levels, and emission and absorption spectra.

44. Physics:Quantum Atomic structure and spectroscopy

45. Physics:Quantum Hydrogen atom

46. Physics:Quantum number

47. Physics:Quantum Multi-electron atoms

48. Physics:Quantum Fine structure

49. Physics:Quantum Hyperfine structure

50. Physics:Quantum Isotopic shift

51. Physics:Quantum defect

52. Physics:Quantum Zeeman effect

53. Physics:Quantum Stark effect

54. Physics:Quantum Spectral lines and series

55. Physics:Quantum Selection rules

56. Physics:Quantum Fermi's golden rule

57. Physics:Quantum beats

5. Wavefunctions and modes (9) Back to index

A quantum wavefunction showing probability amplitude in space; the square of its magnitude gives the probability density.

58. Physics:Quantum Wavefunction

59. Physics:Quantum Superposition principle

60. Physics:Quantum Eigenstates and eigenvalues

61. Physics:Quantum Boundary conditions and quantization

62. Physics:Quantum Standing waves and modes

63. Physics:Quantum Normal modes and field quantization

64. Physics:Number of independent spatial modes in a spherical volume

65. Physics:Quantum Density of states

66. Physics:Quantum carpet

6. Quantum dynamics and evolution (20) Back to index

67. Physics:Quantum Time evolution

68. Physics:Quantum Schrödinger equation

69. Physics:Quantum Time-dependent Schrödinger equation

70. Physics:Quantum Stationary states

71. Physics:Quantum Perturbation theory

72. Physics:Quantum Time-dependent perturbation theory

73. Physics:Quantum Adiabatic theorem

74. Physics:Quantum Berry phase

75. Physics:Quantum Aharonov-Bohm effect

76. Physics:Quantum Scattering theory

77. Physics:Quantum Scattering matrix

78. Physics:Quantum S-matrix

79. Physics:Quantum tunnelling

80. Physics:Quantum speed limit

81. Physics:Quantum revival

82. Physics:Quantum reflection

83. Physics:Quantum oscillations

84. Physics:Quantum jump

85. Physics:Quantum boomerang effect

86. Physics:Quantum chaos

7. Measurement and information (9) Back to index

87. Physics:Quantum Measurement theory

88. Physics:Quantum Measurement operators

89. Physics:Quantum Projective measurement

90. Physics:Quantum POVM

91. Physics:Quantum Weak measurement

92. Physics:Quantum Measurement collapse

93. Physics:Quantum entanglement

94. Physics:Quantum Zeno effect

95. Physics:Quantum limit

8. Quantum information and computing (10) Back to index

96. Physics:Quantum information theory

97. Physics:Quantum Qubit

98. Physics:Quantum Entanglement

99. Physics:Quantum Gates and circuits

100. Physics:Quantum Computing Algorithms in the NISQ Era

101. Physics:Quantum Noisy Qubits

102. Physics:Quantum random access code

103. Physics:Quantum pseudo-telepathy

104. Physics:Quantum network

105. Physics:Quantum money

9. Quantum optics and experiments (5) Back to index

Experimental quantum physics: qubits, dilution refrigerators, quantum communication, and laboratory systems.

106. Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy

107. Physics:Quantum optics beam splitter experiments

108. Physics:Quantum Ultra fast lasers

109. Physics:Quantum Experimental quantum physics

110. Physics:Quantum optics

111. Template:Quantum optics operators

10. Open quantum systems (9) Back to index

112. Physics:Quantum Open systems

113. Physics:Quantum Master equation

114. Physics:Quantum Lindblad equation

115. Physics:Quantum Decoherence

116. Physics:Quantum dissipation

117. Physics:Quantum Markov semigroup

118. Physics:Quantum Markovian dynamics

119. Physics:Quantum Non-Markovian dynamics

120. Physics:Quantum Trajectories

11. Quantum field theory (23) Back to index

Structural dependency map of quantum field theory.

121. Physics:Quantum field theory (QFT) basics

122. Physics:Quantum field theory (QFT) core

123. Physics:Quantum Fields and Particles

124. Physics:Quantum Second quantization

125. Physics:Quantum Fock space

126. Physics:Quantum Harmonic Oscillator field modes

127. Physics:Quantum Creation and annihilation operators

128. Physics:Quantum vacuum fluctuations

129. Physics:Quantum Casimir effect

130. Physics:Quantum Propagators in quantum field theory

131. Physics:Quantum Feynman diagrams

132. Physics:Quantum Path integral formulation

133. Physics:Quantum Renormalization in field theory

134. Physics:Quantum Renormalization group

135. Physics:Quantum Field Theory Gauge symmetry

136. Physics:Quantum Spontaneous symmetry breaking

137. Physics:Quantum Non-Abelian gauge theory

138. Physics:Quantum Electrodynamics (QED)

139. Physics:Quantum chromodynamics (QCD)

140. Physics:Quantum Electroweak theory

141. Physics:Quantum Standard Model

142. Physics:Quantum triviality

143. Physics:Quantum confinement problem

12. Statistical mechanics and kinetic theory (9) Back to index

144. Physics:Quantum Statistical mechanics

145. Physics:Quantum Partition function

146. Physics:Quantum Distribution functions

147. Physics:Quantum Liouville equation

148. Physics:Quantum Kinetic theory

149. Physics:Quantum Boltzmann equation

150. Physics:Quantum BBGKY hierarchy

151. Physics:Quantum Relaxation and thermalization

152. Physics:Quantum Thermodynamics

13. Condensed matter and solid-state physics (15) Back to index

153. Physics:Quantum Band structure

154. Physics:Quantum Fermi surfaces

155. Physics:Quantum Landau levels

156. Physics:Quantum Semiconductor physics

157. Physics:Quantum Phonons

158. Physics:Quantum Electron-phonon interaction

159. Physics:Quantum Exchange interaction

160. Physics:Quantum Superconductivity

161. Physics:Quantum Topological phases of matter

162. Physics:Quantum well

163. Physics:Quantum spin liquid

164. Physics:Quantum spin Hall effect

165. Physics:Quantum phase transition

166. Physics:Quantum critical point

167. Physics:Quantum dot

14. Plasma and fusion physics (8) Back to index

Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.

168. Physics:Quantum Fusion reactions and Lawson criterion

169. Physics:Quantum Plasma (fusion context)

170. Physics:Quantum Magnetic confinement fusion

171. Physics:Quantum Inertial confinement fusion

172. Physics:Quantum Plasma instabilities and turbulence

173. Physics:Quantum Tokamak core plasma

174. Physics:Quantum Tokamak edge physics and recycling asymmetries

175. Physics:Quantum Stellarator

15. Timeline (8) Back to index

176. Physics:Quantum mechanics/Timeline

177. Physics:Quantum mechanics/Timeline/Pre-quantum era

178. Physics:Quantum mechanics/Timeline/Old quantum theory

179. Physics:Quantum mechanics/Timeline/Modern quantum mechanics

180. Physics:Quantum mechanics/Timeline/Quantum field theory era

181. Physics:Quantum mechanics/Timeline/Quantum information era

182. Physics:Quantum mechanics/Timeline/Quantum technology era

183. Physics:Quantum mechanics/Timeline/Quiz

16. Advanced and frontier topics (16) Back to index

184. Physics:Quantum topology

185. Physics:Quantum battery

186. Physics:Quantum Supersymmetry

187. Physics:Quantum Black hole thermodynamics

188. Physics:Quantum Holographic principle

189. Physics:Quantum gravity

190. Physics:Quantum De Sitter invariant special relativity

191. Physics:Quantum Doubly special relativity

192. Physics:Quantum arithmetic geometry

193. Physics:Quantum unsolved problems

194. Physics:Quantum Yang-Mills mass gap

195. Physics:Quantum gravity problem

196. Physics:Quantum black hole information paradox

197. Physics:Quantum dark matter problem

198. Physics:Quantum neutrino mass problem

199. Physics:Quantum matter-antimatter asymmetry problem

References

Author: Harold Foppele

Source attribution: Physics:Quantum Formulas Collection