Hilbert spaces

inner product space that is metrically complete; a Banach space whose norm induces an inner product (follows the parallelogram identity)

theorem

theorem

theorem

method for studying scattering of waves and particles

densely defined operator on a Hilbert space whose domain coincides with that of its adjoint and which equals its adjoint; symmetric operator whose adjoint's domain equals its own domain

theorem in the mathematical formulation of quantum mechanics

trying to map moments to a measure that generates them

mathematical theorem related to real and functional analysis

theorem

Hilbert space equipped with a dense subspace that carries (in addition to the subspace topology) a finer topology such that the inclusion map is continuous

Hilbert space of functions in which point evaluation is a continuous linear functional

complex-valued function

a set of orthonormal bases, where each vector of a given basis has the same overlap with all the vectors of other bases

generalization of a positive-definite matrix

mathematical space representing physical quantum systems

theorem that a smooth enough function near a critical point can be expressed as a quadratic form after a suitable change of coordinates

geodesically complete metric space of non-positive curvature

tensor product space endowed with a special inner product

theorem giving a justification of the Born rule in quantum mechanics