We will now make the above discussion concrete, using the formalism developed in the article on the mathematical formulation of quantum mechanics.

These spaces are of fundamental importance in many areas, including the mathematical formulation of quantum mechanics.

This theorem is of central importance for the mathematical formulation of quantum mechanics.

The mathematical formulations of quantum mechanics are abstract.

The Copenhagen interpretation is an attempt to explain the mathematical formulations of quantum mechanics and the corresponding experimental results.

Additionally, Hilbert's work anticipated and assisted several advances in the mathematical formulation of quantum mechanics.

Using mathematical formulations of quantum mechanics, such as the Schrödinger equation, the wave function can be solved.

This gives rise to the bra-ket notation used by physicists in the mathematical formulation of quantum mechanics.

(See also: Particle in a box, Mathematical formulation of quantum mechanics.)

This section summarizes this relationship, which is stated in terms of the mathematical formulation of quantum mechanics.

Together with the mathematical formulation of quantum mechanics, in large measure due to John von Neumann, this gave the treatment familiar since about 1930.

The Heisenberg picture is an alternative mathematical formulation of quantum mechanics where stationary states are truly mathematically constant in time.

The mathematical formulation of quantum mechanics (QM) is built upon the concept of an operator.

The Hellinger-Toeplitz theorem leads to some technical difficulties in the mathematical formulation of quantum mechanics.

Thus the standard mathematical formulation of quantum mechanics allows different observers to give different accounts of the same sequence of events.

The study of spectra and related properties is known as spectral theory, which has numerous applications, most notably the mathematical formulation of quantum mechanics.

Wigner's theorem, proved by Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics.

In the mathematical formulation of quantum mechanics, any pair of non-commuting self-adjoint operators representing observables are subject to similar uncertainty limits.

The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics.

According to the standard mathematical formulation of quantum mechanics, quantum observables such as 'x' and 'p' should be represented as self-adjoint operators on some Hilbert space.

The significance of the concept of a Hilbert space was underlined with the realization that it offers one of the best mathematical formulations of quantum mechanics.

In mathematical physics, the Dirac-von Neumann axioms give a mathematical formulation of quantum mechanics in terms of operators on a Hilbert space.

In the mathematical formulation of quantum mechanics, a physical system is fully described by a vector in a complex number Hilbert space, the collection of all possible normalizable wavefunctions.

The mathematical formulation of quantum mechanics by Werner Heisenberg and Erwin Schrödinger was originally in terms of unbounded self-adjoint operators on a Hilbert space.

The complex number field is intrinsic to the mathematical formulations of quantum mechanics, where complex Hilbert spaces provide the context for one such formulation that is convenient and perhaps most standard.