Convergent perturbation theory for a q-deformed anharmonic oscillator

被引：0

作者：

Dick R. ^{[1
]}

Pollok-Narayanan A. ^{[1
,2
]}

Steinacker H. ^{[1
]}

Wess J. ^{[1
,2
]}

机构：

[1] Sektion Physik der Ludwig-M., D-80333 München

[2] Max-Planck-Institut für Physik, D-80805 München

来源：

The European Physical Journal C - Particles and Fields | 1999年 / 7卷 / 2期

关键词：

Quantum Mechanic; Perturbation Theory; Perturbation Series; Anharmonic Oscillator; Exact Eigenstates;

D O I：

10.1007/s100529801003

中图分类号：

学科分类号：

摘要：

A q-deformed anharmonic oscillator is defined within the framework of q-deformed quantum mechanics. It is shown that the Rayleigh-Schrödinger perturbation series for the bounded spectrum converges to exact eigenstates and eigenvalues, for q close to 1. The radius of convergence becomes zero in the undeformed limit.

引用

页码：363 / 368

页数：5

共 15 条

[1]

Bender C.M., Wu T.T., Large Order Behavior of Perturbation Theory, PRL, 27, 1, (1971)

[2]

Bender C.M., Wu T.T., Anharmonic Oszillator, Phys. Rev., 184, 5, (1969)

[3]

Loeffel J.J., Martin A., Simon B., Wightman A.S., Pade approximants and the anharmonic oscillator, Physics Letters, 30 B, (1969)

[4]

Fichtmuller M., Lorek A., Wess J., Q-deformed Phase Space and Its Lattice Structure

[5]

Cerchiai B.L., Wess J., q-deformed Minkowski space based on a q-deformed Lorentz algebra, Europ. Journ. of Physics C

[6]

Macfarlane A.J., On q-analogues of the quantum harmonic oscillator and quantum group SU(2)<sub>q</sub>, J. Phys. A, 22, (1989)

[7]

Biedenharn L.C., The quantum group SU<sub>q</sub>(2) and a q-analogue of the boson operators, J. Phys. A, 22, (1989)

[8]

Lorek A., Ruffing A., Wess J., A q-deformation of the Harmonic Oscillator

[9]

Hebecker A., Schreckenberg S., Schwenk J., Weich W., Wess J., Representations of a q-deformed Heisenberg algebra, Z. Phys. C, 64, pp. 355-359, (1994)

[10]

Seifert J., q-deformierte Ein-Teilchen Quantenmechanik, (1996)

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