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2. Position and momentum spaces - Wikipedia

   en.wikipedia.org/wiki/Position_and_momentum_spaces

   Position space (also real space or coordinate space) is the set of all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.) Momentum space is the set of all momentum ...

3. Schrödinger equation - Wikipedia

   en.wikipedia.org/wiki/Schrödinger_equation

   In general, the Hamiltonian to be substituted in the general Schrödinger equation is not just a function of the position and momentum operators (and possibly time), but also of spin matrices. Also, the solutions to a relativistic wave equation, for a massive particle of spin s, are complex-valued 2(2s + 1)-component spinor fields.

4. Canonical commutation relation - Wikipedia

   en.wikipedia.org/wiki/Canonical_commutation_relation

   In quantum mechanics, the canonical commutation relation is the fundamental relation between canonical conjugate quantities (quantities which are related by definition such that one is the Fourier transform of another). For example, between the position operator x and momentum operator px in the x direction of a point particle in one dimension ...

5. Operator (physics) - Wikipedia

   en.wikipedia.org/wiki/Operator_(physics)

   Operator (physics) An operator is a function over a space of physical states onto another space of states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are useful tools in classical mechanics.

6. Uncertainty principle - Wikipedia

   en.wikipedia.org/wiki/Uncertainty_principle

   v. t. e. Canonical commutation rule for position q and momentum p variables of a particle, 1927. pq − qp = h / (2 πi). Uncertainty principle of Heisenberg, 1927. The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with ...

7. Momentum operator - Wikipedia

   en.wikipedia.org/wiki/Momentum_operator

   This operator occurs in relativistic quantum field theory, such as the Dirac equation and other relativistic wave equations, since energy and momentum combine into the 4-momentum vector above, momentum and energy operators correspond to space and time derivatives, and they need to be first order partial derivatives for Lorentz covariance.

8. Conjugate variables - Wikipedia

   en.wikipedia.org/wiki/Conjugate_variables

   In quantum mechanics, conjugate variables are realized as pairs of observables whose operators do not commute. In conventional terminology, they are said to be incompatible observables . Consider, as an example, the measurable quantities given by position ( x ) {\displaystyle \left(x\right)} and momentum ( p ) {\displaystyle \left(p\right)} .

9. Newton's laws of motion - Wikipedia

   en.wikipedia.org/wiki/Newton's_laws_of_motion

   In quantum physics, position and momentum are represented by mathematical entities known as Hermitian operators, and the Born rule is used to calculate the expectation values of a position measurement or a momentum measurement. These expectation values will generally change over time; that is, depending on the time at which (for example) a ...