The two dimensional motion of a particle in an inverse square potential: Classical and quantum aspects

被引：8

作者：

Martinez-y-Romero, R. P. ^{[1
]}

Nunez-Yepez, H. N. ^{[2
]}

Salas-Brito, A. L. ^{[3
]}

机构：

[1] Univ Nacl Autonoma Mexico, Fac Ciencias, Coyoacan 04510, DF, Mexico

[2] Univ Autonoma Metropolitana Iztapalapa, Dept Fis, Mexico City 09340, DF, Mexico

[3] Univ Autonoma Metropolitana Azcapotzalco, Dept Ciencias Basicas, Lab Sistemas Dinam, Coyoacan 04000, DF, Mexico

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2013年 / 54卷 / 05期

关键词：

POLAR-MOLECULES; ONE-DIMENSION; BOUND-STATES; RENORMALIZATION;

D O I：

10.1063/1.4804356

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The classical 2D dynamics of a particle moving under an inverse square potential, -k/r(2), is analysed. We show that such problem is an example of a geometric system since its negative energy orbits are equivalent to free motion on a certain hypersurface. We then solve in momentum space, the corresponding unrenormalized quantum problem showing that there is no discrete energy spectrum and, particularly, no ground state. (C) 2013 AIP Publishing LLC.

引用

页数：7

共 50 条

[1] Classical and quantum motion in an inverse square potential
Avila-Aoki, M.
Cisneros, C.
Martinez-y-Romero, R. P.
Nunez-Yepez, H. N.
Salas-Brito, A. L.
PHYSICS LETTERS A, 2009, 373 (04) : 418 - 421
[2] Comment on "The two dimensional motion of a particle in an inverse square potential: Classical and quantum aspects" [J. Math. Phys. 54, 053509 (2013)]
Bietenholz, Wolfgang
Chryssomalakos, Chryssomalis
Salgado, Marcelo
JOURNAL OF MATHEMATICAL PHYSICS, 2015, 56 (10)
[3] Classical and quantum dynamics in an inverse square potential
Guillaumin-Espana, Elisa
Nunez-Yepez, H. N.
Salas-Brito, A. L.
JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (10)
[4] Falling of a quantum particle in an inverse square attractive potential
Vasyutaa, Vasyl M.
Tkachuk, Volodymyr M.
EUROPEAN PHYSICAL JOURNAL D, 2016, 70 (12):
[5] Falling of a quantum particle in an inverse square attractive potential
Vasyl M. Vasyuta
Volodymyr M. Tkachuk
The European Physical Journal D, 2016, 70
[6] Planar two-particle Coulomb interaction: Classical and quantum aspects
Ghosh, S
PHYSICAL REVIEW D, 1998, 57 (10): : 6342 - 6349
[7] Nuclear quantum effects and classical potential energy surfaces: Two classical quasiparticles per quantum particle
Sinitskiy, Anton
Voth, Gregory
ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY, 2016, 252
[8] INVERSE-SQUARE POTENTIAL AND THE QUANTUM VORTEX
WU, H
SPRUNG, DWL
PHYSICAL REVIEW A, 1994, 49 (06): : 4305 - 4311
[9] TWO-DIMENSIONAL MOTION OF A SLOW QUANTUM PARTICLE IN THE FIELD OF A CENTRAL LONG-RANGE POTENTIAL
Pupyshev, V. V.
THEORETICAL AND MATHEMATICAL PHYSICS, 2019, 199 (03) : 828 - 848
[10] Two-Dimensional Motion of a Slow Quantum Particle in the Field of a Central Long-Range Potential
V. V. Pupyshev
Theoretical and Mathematical Physics, 2019, 199 : 828 - 848

← 1 2 3 4 5 →