Self Adjoint Operators
Mostrando 1-12 de 14 artigos, teses e dissertações.
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1. Singularidades quânticas / Quantum singularities
Espaços-tempo classicamente singulares serão estudados de um ponto de vista quântico. A utilização da mecânica quântica será feita de duas maneiras. A primeira consiste em encontrar a função de onda do Universo, resolvendo a equação de Wheeler-DeWitt para as variáveis canônicas do espaço-tempo. A segunda consiste em acoplar conformemente campo
IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia. Publicado em: 22/08/2011
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2. The time-dependent Schrödinger equation: the need for the Hamiltonian to be self-adjoint
We present some simple arguments to show that quantum mechanics operators are required to be self-adjoint. We emphasize that the very definition of a self-adjoint operator includes the prescription of a certain domain of the operator. We then use these concepts to revisit the solutions of the time-dependent Schroedinger equation of some well-known simple pro
Brazilian Journal of Physics. Publicado em: 2008-03
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3. Quantum singularities associated to topological defects in classically singular spacetimes / Singularidades quanticas associadas a defeitos topologicos em espaços-tempos classicamente singulares
Espaços-tempos classicamente singulares são estudados utilizando-se partículas quânticas (ao invés de clássicas) obedecendo as equações de Klein-Gordon e Dirac, a fim de determinar se estes espaços permanecem singulares do ponto de vista quântico. Primeiramente é apresentada uma revisão do ferramental matemático necessário para o estudo de sing
Publicado em: 2008
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4. ESTADOS SEMICLÁSSICOS NA GRAVIDADE QUÂNTICA / SEMICLASSICAL STATES IN QUANTUM GRAVITY
Loop quantum gravity (LQG) is currently one of the most promising approaches to describing general relativity in quantum terms. One of its key issues is to detect in the quantum theory semiclassical states whose macroscopic properties are the same as those of specific configurations of the classical theory. In this dissertation, we begin by presenting the LQ
Publicado em: 2006
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5. The “Up-Down” Problem For Operator Algebras
It is shown that for any C*-algebra A of operators on a separable Hilbert space, there is, for each self-adjoint operator x in the strong closure of A, a sequence {xn} of self-adjoint operators, each of which is the strong limit of a monotone increasing sequence of self-adjoint operators from A, such that {xn} is monotone decreasing and strongly convergent t
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6. On a Variational Formula for the Principal Eigenvalue for Operators with Maximum Principle
In this paper a variational formula is obtained for the principal eigenvalue for operators with maximum principle. This variational formula does not require the operators to be self-adjoint. But if they are self-adjoint this formula reduces to the classical Rayleigh-Ritz formula.
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7. EIGENFUNCTION EXPANSIONS FOR FORMALLY SELF-ADJOINT PARTIAL DIFFERENTIAL OPERATORS. I
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8. EIGENFUNCTION EXPANSIONS FOR FORMALLY SELF-ADJOINT PARTIAL DIFFERENTIAL OPERATORS. II
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9. TRANSLATION OPERATORS ON THE HALF-LINE
The self-adjoint algebra of operators generated by the semigroup of translation operators acting on the Hilbert space of functions supported on the half-line is studied. A real-valued index is introduced and is used to determine the spectrum of the Wiener-Hopf integral operators with distribution kernel having an almost periodic Fourier transform. Further, t
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10. Generalizations of the classical Weyl and Colin de Verdière's formulas and the orbit method
The classical Weyl formula expresses the leading term of the asymptotics of the counting function N(λ, H) of the spectrum of a self-adjoint operator H in an invariant form: one can “hear” the volume of the subset of the cotangent bundle where the symbol of the operator H is less than λ. In particular, it is applicable to Schrödinger operators with ele
National Academy of Sciences.
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11. The Spectrum of Seminormal Operators
With every pair of bounded self-adjoint operators {U,V} on Hilbert space such that VU - UV = (1/πi)C, where C is trace class, there is associated a certain function of two complex variables called the determining function of the pair. It was previously shown how the determining function can be obtained as the solution of a certain Riemann-Hilbert problem ca
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12. Convergence of quantum electrodynamics in a curved modification of Minkowski space.
The interaction and total hamiltonians for quantum electrodynamics, in the interaction representation, are entirely regular self-adjoint operators in Hilbert space, in the universal covering manifold M of the conformal compactification of Minkowski space Mo. (M is conformally equivalent to the Einstein universe E, in which Mo may be canonically imbedded.) In