Formally exact quantization condition for nonrelativistic quantum systems

被引：32

作者：

Ou, YC ^{[1
]}

Cao, ZQ ^{[1
]}

Shen, QS ^{[1
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Phys, Shanghai 200240, Peoples R China

来源：

JOURNAL OF CHEMICAL PHYSICS | 2004年 / 121卷 / 17期

关键词：

D O I：

10.1063/1.1799015

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

Based on the standard transfer matrix, a formally exact quantization condition for arbitrary potentials, which outflanks and unifies the historical approaches, is derived. It can be used to find the exact bound-state energy eigenvalues of the quantum system without solving an equation of motion for the system wave functions. (C) 2004 American Institute of Physics.

引用

页码：8175 / 8178

页数：4

共 13 条

[1] IS THE LOWEST ORDER SUPERSYMMETRIC WKB APPROXIMATION EXACT FOR ALL SHAPE INVARIANT POTENTIALS [J].

BARCLAY, DT ;

KHARE, A ;

SUKHATME, U .

PHYSICS LETTERS A, 1993, 183 (04) :263-266

[2]

BOHM D, 1952, PHYS REV, V85, P166, DOI 10.1103/PhysRev.85.166

[3] Chaotic dynamics in billiards using Bohm's quantum mechanics [J].

Bonfim, OFD ;

Florencio, J ;

Barreto, FCS .

PHYSICAL REVIEW E, 1998, 58 (03) :R2693-R2696

[4] Exact analytical method for planar optical waveguides with arbitrary index profile [J].

Cao, ZQ ;

Jiang, Y ;

Shen, QS ;

Dou, XM ;

Chen, YL .

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 1999, 16 (09) :2209-2212

[5] Quality of the supersymmetric WKB quantization condition for non-shape-invariant potentials [J].

Chakrabarti, B ;

Das, TK .

PHYSICAL REVIEW A, 1999, 60 (01) :104-111

[6] EXACTNESS OF SEMICLASSICAL BOUND-STATE ENERGIES FOR SUPERSYMMETRIC QUANTUM-MECHANICS [J].

COMTET, A ;

BANDRAUK, AD ;

CAMPBELL, DK .

PHYSICS LETTERS B, 1985, 150 (1-3) :159-162

[7] Phase loss in WKB waves due to reflection by a potential [J].

Friedrich, H ;

Trost, J .

PHYSICAL REVIEW LETTERS, 1996, 76 (26) :4869-4873

[8]

Gaspard P., 1995, Advances in Chemical Physics, V90, P105

[9] Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen [J].

Hainz, J ;

Grabert, H .

PHYSICAL REVIEW A, 1999, 60 (02) :1698-1701

[10] Supershells in metal clusters: Self-consistent calculations and their semiclassical interpretation [J].

Koch, E .

PHYSICAL REVIEW LETTERS, 1996, 76 (15) :2678-2681

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