Gewöhnliche Differentialgleichungen

Heuser, Harro

doi:10.1007/978-3-322-91185-8

Cited by 13 publications

(8 citation statements)

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“…For periodic f the classical theorem of Floquet (see e.g. [10] and [11]) claims that there are particular solutions of equations like (1.12) with the general form e iΩt u(t), where u(t) is periodic with the same period of f . In order to preserve unitarity we must have Ω ∈ R. This form of the particular solutions is called the "Floquet form" and the frequencies Ω are called "secular frequencies".…”

Section: The Floquet Form Of the Wave Function The Fourier Decomposimentioning

confidence: 99%

Convergent Perturbative Solutions of the Schrödinger Equation for Two-Level Systems with Hamiltonians Depending Periodically on Time

Barata¹

2001

Ann. Henri Poincaré

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Abstract. We study the Schrödinger equation of a class of two-level systems under the action of a periodic time-dependent external field in the situation where the energy difference 2ǫ between the free energy levels is sufficiently small with respect to the strength of the external interaction. Under suitable conditions we show that this equation has a solution in terms of converging power series expansions in ǫ. In contrast to other expansion methods, like in the Dyson expansion, the method we present is not plagued by the presence of "secular terms". Due to this feature we were able to prove absolute and uniform convergence of the Fourier series involved in the computation of the wave functions and to prove absolute convergence of the ǫ-expansions leading to the "secular frequency" and to the coefficients of the Fourier expansion of the wave function.

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Section: The Floquet Form Of the Wave Function The Fourier Decomposimentioning

confidence: 99%

Convergent Perturbative Solutions of the Schrödinger Equation for Two-Level Systems with Hamiltonians Depending Periodically on Time

Barata¹

2001

Ann. Henri Poincaré

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“…Einen Überblick über die Theorie von Anfangswertproblemen und die elementar lösbaren Typen finden sich z. B. bei Walter [1] und Heuser [2].…”

Section: Anfangswertprobleme Gewöhnlicher Differenzialgleichungenunclassified

Anfangswertprobleme gewöhnlicher Differenzialgleichungen

Munz¹,

Westermann²

2018

Numerische Behandlung Gewöhnlicher Und Partieller Differenzialgleichungen

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“…can be established (Burg et al, 2013;Heuser, 1995). The entries P ij are continuously differentiable functions for all l ∈ [0, 1].…”

Section: Solution Using Perturbation Theorymentioning

confidence: 99%

A full wave description for thin wire structures with TLST and perturbation theory

2018

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Abstract. A full wave description of a thin wire structure, that includes mutual interactions and radiation, can be obtained in closed form with the so-called Transmission Line Super Theory or a refined variant of this method that utilises perturbation theory. In either procedure, a set of mixed potential integral equations is solved for the currents that propagate along a wire. With the perturbation approach, no iteration is required to approximate the initial current distribution on the wire. This procedure will be applied to solve multi-wire problems. The theory will be derived and computed results will be shown to be in good agreement with method of moment computations.

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Gewöhnliche Differentialgleichungen

Cited by 13 publications

References 0 publications

Convergent Perturbative Solutions of the Schrödinger Equation for Two-Level Systems with Hamiltonians Depending Periodically on Time

Convergent Perturbative Solutions of the Schrödinger Equation for Two-Level Systems with Hamiltonians Depending Periodically on Time

Anfangswertprobleme gewöhnlicher Differenzialgleichungen

A full wave description for thin wire structures with TLST and perturbation theory

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