Nonuniqueness of the phase shift in central scattering due to monodromy

被引：20

作者：

Dullin, Holger R. ^{[1
]}

Waalkens, Holger ^{[2
,3
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

[2] Univ Groningen, Dept Math, NL-9747 AG Groningen, Netherlands

[3] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

来源：

PHYSICAL REVIEW LETTERS | 2008年 / 101卷 / 07期

关键词：

D O I：

10.1103/PhysRevLett.101.070405

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Scattering at a central potential is completely characterized by the phase shifts which are the differences in phase between outgoing scattered and unscattered partial waves. In this Letter, it is shown that, for 2D scattering at a repulsive central potential, the phase shift cannot be uniquely defined due to a topological obstruction which is similar to monodromy in bound systems.

引用

页数：4

共 11 条

[1]

ARNOLD VI, 1978, GRADUATE TEXTS MATH, V60

[2] THE QUANTUM-MECHANICAL SPHERICAL PENDULUM [J].

CUSHMAN, R ;

DUISTERMAAT, JJ .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 19 (02) :475-479

[3]

Cushman R.H., 2015, Global Aspects of Classical Integrable Systems, V2nd ed.

[4] Monodromy in perturbed Kepler systems: Hydrogen atom in crossed fields [J].

Cushman, RH ;

Sadovskii, DA .

EUROPHYSICS LETTERS, 1999, 47 (01) :1-7

[5] CO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy -: art. no. 024302 [J].

Cushman, RH ;

Dullin, HR ;

Giacobbe, A ;

Holm, DD ;

Joyeux, M ;

Lynch, P ;

Sadovskií, DA ;

Zhilinskií, BI .

PHYSICAL REVIEW LETTERS, 2004, 93 (02) :024302-1

[6] ON GLOBAL ACTION-ANGLE COORDINATES [J].

DUISTERMAAT, JJ .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1980, 33 (06) :687-706

[7]

Einstein A, 1917, VERHAND DEUT PHYS GE, V19, P82

[8]

Froman N., 1965, JWKB APPROXIMATION C

[9]

Goldstein H., 2002, CLASSICAL MECH

[10] Monodromy, diabolic points, and angular momentum coupling [J].

Sadovskií, D ;

Zhilinskií, BI .

PHYSICS LETTERS A, 1999, 256 (04) :235-244

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