List of equations in quantum mechanics
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equation In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in F ...
s in the theory of
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
.


Wavefunctions

A fundamental
physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant ...
occurring in quantum mechanics is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
, ''h''. A common abbreviation is , also known as the ''reduced Planck constant'' or ''Dirac constant''. The general form of
wavefunction A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
for a system of particles, each with position r''i'' 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 In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Pa ...
reduces to an
ordinary derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
.


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.


The Hydrogen atom


See also

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Defining equation (physical chemistry) In physical chemistry, there are numerous quantities associated with chemical compounds and reactions; notably in terms of ''amounts'' of substance, ''activity'' or ''concentration'' of a substance, and the ''rate'' of reaction. This article use ...
*
List of electromagnetism equations This article summarizes equations in the theory of electromagnetism. Definitions Here subscripts ''e'' and ''m'' are used to differ between electric and magnetic charges. The definitions for monopoles are of theoretical interest, although re ...
*
List of equations in classical mechanics Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. The sub ...
*
List of equations in fluid mechanics This article summarizes equations in the theory of fluid mechanics. Definitions Here \mathbf \,\! is a unit vector in the direction of the flow/current/flux. Equations See also * Defining equation (physical chemistry) *List of electro ...
*
List of equations in gravitation This article summarizes equations in the theory of gravitation. Definitions Gravitational mass and inertia A common misconception occurs between centre of mass and centre of gravity. They are defined in similar ways but are not exactly the ...
*
List of equations in nuclear and particle physics This article summarizes equations in the theory of nuclear physics and particle physics. Definitions Equations Nuclear structure Nuclear decay Nuclear scattering theory The following apply for the nuclear reaction: :''a'' + ''b'' ...
*
List of equations in wave theory This article summarizes equations in the theory of waves. Definitions General fundamental quantities A wave can be longitudinal where the oscillations are parallel (or antiparallel) to the propagation direction, or transverse where the oscill ...
*
List of photonics equations This article summarizes equations used in optics, including geometric optics, physical optics, radiometry, diffraction, and interferometry. Definitions Geometric optics (luminal rays) General fundamental quantities Physical optics (EM l ...
*
List of relativistic equations Following is a list of the frequently occurring equations in the theory of special relativity. Postulates of Special Relativity To derive the equations of special relativity, one must start with two other #The laws of physics are invariant ...


Footnotes


Sources

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Further reading

* * * * {{SI units navbox Physical quantities SI units Physical chemistry Equations of physics