
	Where results make sense

Topic: Complex Hilbert space

Related Topics

Tack

Peshtigo (town), Wisconsin

ECN

John Haywood

In the News (Sun 27 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Hilbert space - Wikipedia, the free encyclopedia
		In mathematics, a Hilbert space is a generalization of Euclidean space that is not restricted to finite dimensions.
		Hilbert spaces are of crucial importance in the mathematical formulation of quantum mechanics.
		Of all the infinite-dimensional topological vector spaces, the Hilbert spaces are the most "well-behaved" and the closest to the finite-dimensional spaces.
	en.wikipedia.org /wiki/Hilbert_space (2114 words)

	Projective Hilbert space - Wikipedia, the free encyclopedia
		In mathematics and the foundations of quantum mechanics, the projective Hilbert space P(H) of a complex Hilbert space H is the set of equivalence classes of vectors v in H, with v ≠ 0, for the relation given by
		The physical significance of the projective Hilbert space is that in quantum theory, the wave functions ψ and λψ represent the same physical state, for any λ ≠ 0.
		Complex projective Hilbert space may be given a natural metric, the Fubini-Study metric.
	en.wikipedia.org /wiki/Projective_Hilbert_space (299 words)

	Hilbert Space
		Hilbert space is not a space of simple points, rather it is a space of functions at a higher level of mathematical abstraction.
		Rather, Hilbert space is a mathematical device for arranging pieces of information, with each complex coordinate representing a possibility, or probability amplitude, for a given quantum state that might correspond to a definite eigenvalue for energy, or position, or momentum, or spin, etc. Note, that not all of these observable properties can be definite simultaneously.
		The angular momentum of a particle relative to a direction in space is incompatible with the angle of rotation of that particle in a plane perpendicular to that direction in space.
	www.qedcorp.com /pcr/pcr/hilberts.html (2670 words)

	Encyclopedia :: encyclopedia : Hilbert space (Site not responding. Last check: 2007-10-30)
		Hilbert spaces serve to clarify and generalize the concept of Fourier expansion and certain linear transformations such as the Fourier transform.
		Hilbert spaces are of crucial importance in the mathematical formulation of quantum mechanics, although many basic features of quantum mechanics can be understood without going into details about Hilbert spaces.
		We call H a Hilbert space if it is complete with respect to this norm.
	www.hallencyclopedia.com /Hilbert_space (1718 words)

	Hilbert_space
		In mathematics, a Hilbert space is a generalization of Euclidean space which is not restricted to finite dimensions.
		Hilbert spaces provide a context with which to formalize and generalize the concepts of the Fourier series in terms of arbitrary orthogonal polynomials and of the Fourier transform, which are central concepts from functional analysis.
		The name "Hilbert space" was soon adopted by others, for example by Hermann Weyl in his book The Theory of Groups and Quantum Mechanics published in 1931 (English language paperback ISBN 0486602699).
	www.brainyencyclopedia.com /encyclopedia/h/hi/hilbert_space.html (1924 words)

	Mathematical formulation of quantum mechanics - Wikipedia, the free encyclopedia
		In it, he introduced the bra-ket notation, together with an abstract formulation in terms of the Hilbert space used in functional analysis, and showed that Schödinger's and Heisenberg's approaches were two different representations of the same theory.
		A classical description can be given in a fairly direct way by a phase space model of mechanics: states are points in a symplectic phase space, observables are real-valued functions on it, time evolution is given by a one-parameter group of symplectic transformations of the phase space, and physical symmetries are realized by symplectic transformations.
		A quantum description consists of a Hilbert space of states, observables are self adjoint operators on the space of states, time evolution is given by a one-parameter group of unitary transformations on the Hilbert space of states, and physical symmetries are realized by unitary transformations.
	en.wikipedia.org /wiki/Mathematical_formulation_of_quantum_mechanics (3470 words)

	Wikinfo \| Hilbert space (Site not responding. Last check: 2007-10-30)
		The elements of Hilbert spaces are sometimes called "vectors"; they are typically sequences or functions.
		An important concept is that of an orthonormal basis of a Hilbert space H: a subset B of H with three properties:
		Since all separable Hilbert spaces are isomorphic, and since almost all Hilbert spaces used in physics are separable, when physisists talk about the Hilbert space they mean any separable one.
	www.wikinfo.org /wiki.php?title=Hilbert_space (1609 words)

	Kit Chan's Annotated Bibliograhy
		On a separable infinite dimensional complex Hilbert space, we show that the set of hypercyclic operators is dense in the strong operator topology, and moreover the linear span of hypercyclic operators is dense in the operator norm topology.
		We show that the translation operator on a Hilbert space of entire functions of slow growth is hypercyclic, which means that there is a function in the space whose translates are dense.
		For the Dirichlet space of a finitely connected region, we study the structure of its subspaces that are invariant under the algebra of multiplication operators.
	personal.bgsu.edu /~kchan/docs/biblio.html (1091 words)

	Hilbert Space -- Recommendations and Resources (Site not responding. Last check: 2007-10-30)
		Formally, a rigged Hilbert space consists of a Hilbert space ''H'', together with a subspace Φ which carries a finer topology, that is one for which the natural inclusion :
		In mathematics, a semi-Hilbert space is a generalisation of a Hilbert space in functional analysis, in which, roughly speaking, the inner product is required only to be positive semi-definite rather than positive definite, so that it gives rise to a seminorm rather than a vector space norm.
		The quotient of this space by the kernel of this seminorm is also required to be a Hilbert space in the usual sense.
	www.becomingapediatrician.com /health/74/hilbert-space.html (1059 words)

	ON QUANTUM THEORETICAL ORIGINS OF NEWTONIAN TIME
		Notice that the complexity of such a model is contained in its dimensional parameter, and not in a measure of physical extension that exceeds tolerable fluctuations of the Planck regime.
		Hilbert space, it is unitarily equivalent to that representation induced in the Hilbert space of holomorphic functions on CÂ² by the SU(2) rotations in CÂ².
		Such a Hilbert space is that often used for the construction of the all the finite dimensional IRREPS of sl(2, C).
	graham.main.nc.us /~bhammel/PHYS/newtqtime.html (15422 words)

	Hilbert Space
		A hilbert space (biography) is a banach space with a dot product.
		Thus far, a banach space could have any norm, but in a hilbert space, the norm is tied to the dot product.
		If s is a complex vector space it is certainly a real vector space, and the distance metric is unchanged, thus s becomes a real vector space that is also a complete metric space, i.e.
	www.mathreference.com /top-ban,hilbert.html (1106 words)

	math lessons - Schrödinger equation
		In the mathematical formulation of quantum mechanics, each system is associated with a complex Hilbert space such that each instantaneous state of the system is described by a unit vector in that space.
		In this situation, the Schrödinger equation may be conveniently reformulated as a partial differential equation for a wavefunction, a complex scalar field that depends on position as well as time.
		In this case, the state space is the space of all square-integrable complex functions.
	www.mathdaily.com /lessons/Schr%f6dinger_equation (1264 words)

	No Title
		We use a diffusion in a Hilbert space to construct the heat kernel measure
		Then it is proved that holomorphic polynomials on the group are square integrable with respect to the heat kernel measure.
		It is proved that there is an isometry from the first space to the second one.
	icarus.math.mcmaster.ca /gordina/list_of_pub/list_of_pub.html (413 words)

	A theory of concepts and their combinations II: A Hilbert space representation
		Design/methodology/approach - The set of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics.
		Findings - The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept.
		Using the tensor product, a natural product in Hilbert space mathematics, a procedure for describing combined concepts is elaborated.
	repositories.cdlib.org /postprints/538 (282 words)

	PlanetMath: Hilbert module
		See Also: Hilbert space, finitely generated projective module
		Cross-references: -homomorphism, Hilbert* space, complex, complete, norm, positive, pairing, inner product, right
		This is version 5 of Hilbert module, born on 2002-08-30, modified 2004-04-16.
	planetmath.org /encyclopedia/PreHilbertModule.html (97 words)

	Interpolation on the Complex Hilbert Sphere - Menegatto (ResearchIndex)
		Interpolation on the Complex Hilbert Sphere - Menegatto (ResearchIndex)
		Interpolation On The Complex Hilbert Sphere Using Positive..
		Menegatto, V. A., Interpolation on the complex Hilbert sphere, Approx.
	citeseer.ist.psu.edu /420162.html (563 words)

	Quantum Logic and Probability Theory
		It is uncontroversial (though remarkable) that the formal apparatus of quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over by the "quantum logic" of projection operators on a Hilbert space.
		In quantum mechanics, the state space is the (projective) unit sphere S = S(H) of a Hilbert space.
		The upshot of the foregoing discussion is that most test spaces can't be embedded into any classical test space, and that even where such an embedding exists, it typically fails to account for some of the model's states.
	plato.stanford.edu /entries/qt-quantlog (7978 words)

	symplectic
		They are two real forms of the same complex simple Lie group, and there really is a profound conceptual connection between symplectic structures and quaternions that's responsible for this "coincidence".
		The 2-dimensional complex Hilbert space of spinors, H, is secretly a 1-dimensional quaternionic Hilbert space!
		But the Hilbert space of the spin-1/2 particle isn't canonically identified with the quaternions - it doesn't have any god-given element "1" for example.
	math.ucr.edu /home/baez/symplectic.html (2392 words)

	Interpolation On The Complex Hilbert Sphere Using Positive Definite And Conditionally Negative Definite Kernels - ...
		INTRODUCTION Let S 1 be the unit sphere of the complex Hilbert space ` 2.
		Menegatto, V. A., Interpolation on the complex Hilbert sphere using positive definite and conditionally negative definite kernels, Acta Math.
		2 Interpolation on the complex Hilbert sphere - Menegatto - 1996
	citeseer.ist.psu.edu /403767.html (540 words)

	FIELDS ON NONCOMMUTATIVE SPACES
		(n) be a complex Hilbert space of dimension n, and
		is a complex vector space with a multiplication '' that can be specified as follows: is a binary operation on
		is an element of the dual space of
	graham.main.nc.us /~bhammel/PHYS/flds.html (330 words)

	Hilbert Space (Site not responding. Last check: 2007-10-30)
		DEFINITION: A Hilbert space is an inner product space which, as a metric space, is complete.
		As the example above shows, the space of rational numbers, with the usual notion of distance, is not a complete metric space.
		You should now compare these representations with those for a finite dimensional vector space, and convince yourself that these two sets are formally identical.
	www.chem.brown.edu /chem277/Tan_on_Hilbert_Space.html (1211 words)

	Cogprints - A theory of concepts and their combinations II: A Hilbert space representation (Site not responding. Last check: 2007-10-30)
		The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics.
		The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept.
		By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented.
	cogprints.org /4771 (187 words)

	Alternative structures and bi-Hamiltonian systems on a Hilbert space
		unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space.
		The group of bi-unitary transformations is considered in both the generic and the non-generic case.
		Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems.
	stacks.iop.org /0305-4470/38/3813 (304 words)

	Citebase - Commutativity up to a factor of bounded operators in complex Hilbert space
		Commutativity up to a factor of bounded operators in complex Hilbert space
		Authors: Brooke, J. Busch, P. Pearson, D. We explore commutativity up to a factor, AB=λ BA, for bounded operators in a complex Hilbert space.
		Conditions on the possible values of the factor λ are formulated and shown to depend on spectral properties of the operators involved.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0007049 (159 words)

	Proving a relation is a partial order
		This relation says that a self-adjoint, bounded, linear operator is greater than another operator of the same category if and only if the inner product of that operator with an arbitrary element in the complex Hilbert space is larger.
		is the identity operator on the complex Hilbert space.
		If you have two normed linear spaces X and Y and you also have a surjective linear map T such that
	www.physicsforums.com /showthread.php?t=91628 (1836 words)

	Quantum mechanics as an approximation to classical mechanics in Hilbert space
		Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite.
		These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics.
		Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around.
	stacks.iop.org /0305-4470/36/L329 (281 words)

	A few polynomial equations
		(5) a bounded linear transformation V of a complex Hilbert space is a partial isometry if and only if
		(7) using a polar decomposition of a bounded linear transformation of a complex Hilbert space T is equivalent to introducing bounded linear transformations P and V such that T= PV,
		We can summarize the above examples by saying that a number of properties of matrices and operators (bounded linear transformations of complex Hilbert space) are equivalent to the statement that a tuple of matrices (or tuple of operators) is a common zero of a set of polynomial equations.
	math.ucsd.edu /~ncalg/StrategyPaper/node5.html (375 words)

Try your search on: Qwika (all wikis)