Superintegrable quantum mechanical systems with position dependent masses invariant with respect to three parametric Lie groups

被引：1

作者：

Nikitin, A. G. ^{[1
,2
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Math, 3 Tereshchenkivska St, UA-01024 Kiev 4, Ukraine

[2] Univ Piemonte Orientale, Dipartimento Sci & Innovaz Tecnol, Viale T Michel 11, I-15121 Alessandria, Italy

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2023年 / 64卷 / 11期

关键词：

SYMMETRIES;

D O I：

10.1063/5.0147792

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Quantum mechanical systems with position dependent masses (PDM) admitting four and more dimensional symmetry algebras are classified. Namely, all PDM systems are specified which, in addition to their invariance with respect to a three parametric Lie group, admit at least one second order integral of motion. The presented classification is partially extended to the more generic systems which admit one or two parametric Lie groups.

引用

页数：18

共 15 条

[1] Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups
Nikitin, A. G.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2023, 56 (39)
[2] Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 1. Systems with cylindric symmetry
Nikitin, A. G.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2024, 57 (26)
[3] Superintegrable and Scale-Invariant Quantum Systems with Position-Dependent Mass
A. G. Nikitin
Ukrainian Mathematical Journal, 2022, 74 : 405 - 419
[4] Superintegrable and Scale-Invariant Quantum Systems with Position-Dependent Mass
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UKRAINIAN MATHEMATICAL JOURNAL, 2022, 74 (03) : 405 - 419
[5] Superintegrable and shape invariant systems with position dependent mass
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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2015, 48 (33)
[6] On the controllability of systems on compact Lie groups and quantum mechanical systems
D'Alessandro, D
PROCEEDINGS OF THE 39TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5, 2000, : 3982 - 3987
[7] Bound states in quantum systems with position dependent effective masses
Plastino, AR
Puente, A
Casas, M
Garcias, F
Plastino, A
REVISTA MEXICANA DE FISICA, 2000, 46 (01) : 78 - 84
[8] Remarks on supersymmetry of quantum systems with position-dependent effective masses
Dutra, AD
Hott, M
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EUROPHYSICS LETTERS, 2003, 62 (01): : 8 - 13
[9] General methods to control right-invariant systems on compact Lie groups and multilevel quantum systems
D'Alessandro, Domenico
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (39)
[10] POSITION DEPENDENT EFFECTIVE MASSES FOR DONOR BINDING ENERGIES IN QUANTUM CONFINED SYSTEMS IN AN ELECTRIC FIELD
Rajashabala, S.
Raman, Kannan
INTERNATIONAL JOURNAL OF NANOSCIENCE, 2010, 9 (1-2) : 83 - 91

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