Quantum Mechanics I

Galindo, Alberto; Pascual, P.

doi:10.1007/978-3-642-83854-5

Cited by 278 publications

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“…(2) for times s that lie outside the support ofḢ(s). Assuming a gap condition and smoothness (or analyticity) of H(s) it has been shown [23,24,11,35,43] that the adiabatic theorem Eq. (2) holds with γ = ∞.…”

Section: Adiabatic Theorems Beyond All Ordersmentioning

confidence: 99%

An Adiabatic Theorem without a Gap Condition

Avron¹,

Elgart²

1999

Mathematical Results in Quantum Mechanics

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We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. The general result we prove gives no information on the rate at which the adiabatic limit is approached. With additional spectral information one can also estimate this rate.

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Section: Adiabatic Theorems Beyond All Ordersmentioning

confidence: 99%

An Adiabatic Theorem without a Gap Condition

Avron¹,

Elgart²

1999

Mathematical Results in Quantum Mechanics

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“…The theory of tensor harmonics on the sphere S 2 is a very well-known subject [39][40][41]. In this section we recast it into the GS notation, which is particularly useful for the type of algebraic computations that must be performed in high-order perturbation theory.…”

Section: Tensor Harmonicsmentioning

confidence: 99%

Second- and higher-order perturbations of a spherical spacetime

2006

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The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory. The GS harmonics are generalized to an arbitrary number of indices on the unit sphere and a formula is given for their products. The formalism is optimized for its implementation in a computer-algebra system, something that becomes essential in practice given the size and complexity of the equations. All evolution equations for the second-order perturbations, as well as the conservation equations for the energy-momentum tensor at this perturbation order, are given in covariant form, in Regge-Wheeler gauge.

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“…A bem da verdade, os estados estacionários de uma partícula em um potencial delta duplo ocupa as páginas de muitos livros-texto [6][7][8][9][10][11][12]. Os possíveis estados ligados são encontrados pela localização dos polos complexos da amplitude de espalhamento ou por meio de uma solução direta da equação de Schrödinger baseada na descontinuidade da derivada primeira da autofunção, mais a continuidade da autofunção e seu bom comportamento assintótico.…”

Section: Introductionunclassified

Estados ligados em um potencial delta duplo via transformada de Laplace

Castro

2012

Rev. Bras. Ensino Fís.

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O problema de estados ligados em um potencial delta duploé revisto com o uso do método da transformada de Laplace. Bem diferentemente de métodos diretos, nenhum conhecimento acerca da descontinuidade de salto da derivada primeira da autofunçãoé requerida para se determinar a solução. Palavras-chave: duplo delta, estado ligado, transformada de Laplace.The problem of bound states in a double delta potential is revisited by means of Laplace transform method. Quite differently from direct methods, no knowledge about the jump discontinuity of the first derivative of the eigenfunction is required to determine the solution.

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Quantum Mechanics I

Abstract: Softcover reprint of the hardcover 1st edition 1990The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cited by 278 publications

References 0 publications

An Adiabatic Theorem without a Gap Condition

An Adiabatic Theorem without a Gap Condition

Second- and higher-order perturbations of a spherical spacetime

Estados ligados em um potencial delta duplo via transformada de Laplace

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