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Results tagged with hilbert-space
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user 124266
This tag is for questions relating to Hilbert Space, a vector space equipped with an inner product, an operation that allows defining lengths and angles, and the space is complete. It arises naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces having the property that it is complete. Applies also to pre-Hilbert spaces, rigged Hilbert spaces, and spaces with negative norm or zero-norm states.
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QED in Minkowski space VS a finite volume and their mathematical formulations
I am currently trying to figure out the relationship between two different presentations of non-interacting quantum electrodynamics. The first is the usual Fock space formulation in infinite Minkowski …
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Why can we not define states of definite position/momentum?
In classical mechanics one thinks of points in phase space as states, all the while knowing that for the precise description of any real physical system one will inevitably have to deal with uncertain …
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Bounds on Matrix Elements of Unbounded Operators
Let $H$ be a separable Hilbert space und $T$ a possibly unbounded densely defined linear operator. (One could probably assume that it's ess. self-adjoint but I would like to avoid this assumption.)
Le …
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Minimum uncertainty Gaussians as basis for Hilbert space?
There are several different concepts of "basis of a vector space" used in physics and rarely distinguished, in particular the context of quantum mechanics. The most important one is "Orthonormal Basis …
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Completeness relation for coherent states of the quantum harmonic oscillator
For the Quantum harmonic oscillator with energy eigenstates $|n\rangle$ one defines a coherent state for every complex number $z$ by setting (note that the normalization varies across the literature)
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Meaning of localization of wave function?
To adress the question as clarified in the comments, I will explain what the standard formalism of quantum Mechanics gives rise to for the observables of position and momentum.
I assume that the stan …
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Why is the general solution of Schrodinger's equation a linear combination of the eigenfunct...
Maybe to answer your question it is useful to start from a slightly different perspective, conceptually. In Quantum Mechanics a system is described by giving a Hilbert space, whose vectors represent s …
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