Self Adjoint Operator
Mostrando 1-8 de 8 artigos, teses e dissertações.
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1. Confinamento de partículas quânticas a curvas do espaço
In this work we study dimensional reductions in some quantum systems; such reductions occur due to confinement of the particle from a tube in space to a curve. Our main goal is to find the effective hamiltonian operator that describes the motion of the particle after confinement. We consider three particular situations. (1) In the first situation, we study a
Publicado em: 2010
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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. O átomo de hidrogênio em 1, 2 e 3 dimensões
In this work we study the Hamiltonian of the hydrogen atom in 1, 2 and 3 dimensions. Especifically, it is defined as a self-adjoint operator in the Hilbert space L2(Rn), n = 1, 2, 3. Nevertheless, the main goal is to study the hydrogen atom 1-D. Particularly, for this is model we address some problens related to the singularity of the Coulomb potential.
Publicado em: 2007
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4. 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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5. THE EIGENFUNCTION EXPANSION THEOREM FOR THE GENERAL SELF-ADJOINT SINGULAR ELLIPTIC PARTIAL DIFFERENTIAL OPERATOR. I. THE ANALYTICAL FOUNDATION1
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6. Self-adjointness of the Fourier expansion of quantized interaction field Lagrangians
Regularity properties significantly stronger than were previously known are developed for four-dimensional non-linear conformally invariant quantized fields. The Fourier coefficients of the interaction Lagrangian in the interaction representation—i.e., evaluated after substitution of the associated quantized free field—is a densely defined operator on th
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7. 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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8. 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