Analytic bounds on transmission probabilities

被引：26

作者：

Boonserm, Petarpa ^{[1
]}

Visser, Matt ^{[2
]}

机构：

[1] Chulalongkorn Univ, Dept Math, Fac Sci, Bangkok 10330, Thailand

[2] Victoria Univ Wellington, Sch Math Stat & Operat Res, Wellington, New Zealand

来源：

ANNALS OF PHYSICS | 2010年 / 325卷 / 07期

关键词：

Transmission; Reflection; Bogoliubov coefficients; Analytic bounds; ONE-DIMENSIONAL SCATTERING; EQUATIONS; VACUUM;

D O I：

10.1016/j.aop.2010.02.005

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We develop some new analytic bounds on transmission probabilities (and the related reflection probabilities and Bogoliubov coefficients) for generic one-dimensional scattering problems. To do so we rewrite the Schrodinger equation for some complicated potential whose properties we are trying to investigate in terms of some simpler potential whose properties are assumed known, plus a (possibly large) "shift" in the potential. Doing so permits us to extract considerable useful information without having to exactly solve the full scattering problem. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1328 / 1339

页数：12

共 34 条

[1] NEW APPROACH TO PERTURBATION-THEORY [J].

AHARONOV, Y ;

AU, CK .

PHYSICAL REVIEW LETTERS, 1979, 42 (24) :1582-1585

[2]

[Anonymous], 2003, Quantum Theory of Tunneling

[3] Probing semiclassical analog gravity in Bose-Einstein condensates with widely tunable interactions -: art. no. 053613 [J].

Barceló, C ;

Liberati, S ;

Visser, M .

PHYSICAL REVIEW A, 2003, 68 (05) :14

[4] Integral equations of scattering in one dimension [J].

Barlette, VE ;

Leite, MM ;

Adhikari, SK .

AMERICAN JOURNAL OF PHYSICS, 2001, 69 (09) :1010-1013

[5] Scattering by one-dimensional smooth potentials: between WKB and Born approximation [J].

Bliokh, KY ;

Freilikher, VD ;

Makarov, NM .

PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES, 2005, 27 (1-2) :262-269

[6]

Bohm D., 1989, Quantum Theory

[7] Bounding the Bogoliubov coefficients [J].

Boonserm, Petarpa ;

Visser, Matt .

ANNALS OF PHYSICS, 2008, 323 (11) :2779-2798

[8] Bounding the greybody factors for Schwarzschild black holes [J].

Boonserm, Petarpa ;

Visser, Matt .

PHYSICAL REVIEW D, 2008, 78 (10)

[9] Transmission probabilities and the Miller-Good transformation [J].

Boonserm, Petarpa ;

Visser, Matt .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (04)

[10]

BRANSON BH, 2000, QUANTUM MECH

← 1 2 3 4 →