Quantum-mechanical solution for the double oscillator in a box

Aguilera‐Navarro, V. C.; Iwamoto, Hiroaki; Koo, Eugenio Ley; Zímerman, A. H.

doi:10.1007/bf02721254

Cited by 8 publications

(4 citation statements)

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“…The Harmonic Oscillator. This particular problem has attracted some attention by Aguilera-Navarro et al [2], Consortini and Frieden [14], Marin and Cruz [54], and Vawter [62]. By means of the Green function for the harmonic oscillator we obtain for the Green function in the box a < x < b Eq.…”

Section: Boundary Problems In Half-spacementioning

confidence: 97%

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δ‐function perturbations and boundary problems by path integration

Grosche

1993

Annalen der Physik

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Abstract. A wide class of boundary problems in quantum mechanics is discussed by using path integrals. This includes motion in half-spaces, radial boxes, rings, and moving boundaries. As a preparation the formalism for the incorporation of δ-function perturbations is outlined, which includes the discussion of multiple δ-function perturbations, δ-function perturbations along perpendicular lines and planes, and moving δ-function perturbations. The limiting process, where the strength of the δ-function perturbations gets infinite repulsive, has the effect of producing impenetrable walls at the locations of the δ-function perturbations, i.e. a consistent description for boundary problems with Dirichlet boundary-condition emerges. Several examples illustrate the formalism.

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Section: Boundary Problems In Half-spacementioning

confidence: 97%

“…For instance, numerical studies can be found in Refs. [2,14,54,62] for the problem of an oscillator in a box.…”

Section: Introductionmentioning

confidence: 99%

δ‐function perturbations and boundary problems by path integration

Grosche

1993

Annalen der Physik

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“…Fig. 1 shows the ground-state energy for β = 1/2 calculated by means of perturbation theory, the LSF method and the variational function (15) for small and moderate values of λ. Fig.…”

Section: Resultsmentioning

confidence: 99%

“…2 shows the results of the latter two approaches for a wider range of values of λ. We appreciate the accuracy of the energy provided by the simple variational function (15) for all values of λ. The reader will find all the necessary details about the LSF collocation method elsewhere [25].…”

Section: Resultsmentioning

confidence: 99%

Harmonic oscillator in a one-dimensional box

Amore,

Fernandez

2009

Preprint

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We study a harmonic molecule confined to a one-dimensional box with impenetrable walls. We explicitly consider the symmetry of the problem for the cases of different and equal masses. We propose suitable variational functions and compare the approximate energies given by the variation method and perturbation theory with accurate numerical ones for a wide range of values of the box length. We analyze the limits of small and large box size.

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