# Momentum - Quantum Mechanics

Quantum Mechanics

Further information: Momentum operator

In quantum mechanics, momentum is defined as an operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once. In quantum mechanics, position and momentum are conjugate variables.

For a single particle described in the position basis the momentum operator can be written as

where ∇ is the gradient operator, ħ is the reduced Planck constant, and i is the imaginary unit. This is a commonly encountered form of the momentum operator, though the momentum operator in other bases can take other forms. For example, in the momentum basis the momentum operator is represented as

where the operator p acting on a wave function ψ(p) yields that wave function multiplied by the value p, in an analogous fashion to the way that the position operator acting on a wave function ψ(x) yields that wave function multiplied by the value x.

For both massive and massless objects, relativistic momentum is related to the de Broglie wavelength λ by

Electromagnetic radiation (including visible light, ultraviolet light, and radio waves) is carried by photons. Even though photons (the particle aspect of light) have no mass, they still carry momentum. This leads to applications such as the solar sail. The calculation of the momentum of light within dielectric media is somewhat controversial (see Abraham–Minkowski controversy).

### Other articles related to "quantum mechanics, quantum, mechanics":

Leggett–Garg Inequality
... the state itself, or on the subsequent system dynamics." In quantum mechanics, the Leggett–Garg inequality is violated, meaning that the time evolution of a system ... Here quantum entanglement plays the central role ... not be obtained in the standard Copenhagen Interpretation of quantum mechanics in its various formulations ...
Quantum Mechanics - Examples - Harmonic Oscillator
... Main article Quantum harmonic oscillator As in the classical case, the potential for the quantum harmonic oscillator is given by This problem can be solved either by solving the Schrödi ...
Bohmian - History - De Broglie–Bohm Theory
... After publishing a popular textbook on Quantum Mechanics which adhered entirely to the Copenhagen orthodoxy, Bohm was persuaded by Einstein to take a critical look at von Neumann's theorem ... The result was 'A Suggested Interpretation of the Quantum Theory in Terms of "Hidden Variables" I and II' ... in the way Brownian motion disturbs Newtonian mechanics) ...
Superstring Theory - Integrating General Relativity and Quantum Mechanics
... situations involving large mass objects in fairly large regions of spacetime whereas quantum mechanics is generally reserved for scenarios at the atomic scale (small spacetime ... unit of length) lengths, general relativity predicts a smooth, flowing surface, while quantum mechanics predicts a random, warped surface, neither of which are anywhere near compatible ... length, with extremely small variances, which completely ignores the quantum mechanical predictions of Planck-scale length dimensional warping ...

### Famous quotes containing the words mechanics and/or quantum:

It is only the impossible that is possible for God. He has given over the possible to the mechanics of matter and the autonomy of his creatures.
Simone Weil (1909–1943)

A personality is an indefinite quantum of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite quantum of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.
Hubert C. Heffner (1901–1985)