TIME-INDEPENDENT METHODS IN CLASSICAL MECHANICS - CALCULATION OF INVARIANT TORI AND SEMI-CLASSICAL ENERGY-LEVELS VIA CLASSICAL VAN VLECK TRANSFORMATIONS

被引:78
作者
JAFFE, C [1 ]
REINHARDT, WP [1 ]
机构
[1] NBS,JOINT INST LAB ASTROPHYS,BOULDER,CO 80309
关键词
D O I
10.1063/1.438538
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
Recently introduced methods for semiclassical quantization of nonseparable systems implicitly or explicitly rely on the existence of the invariant tori of time-independent classical mechanics. We present an accelerated convergence scheme for calculation of such tori based on the classical limit of the Van Vleck transformation, and give theoretical and computational comparisons with the methods of Percival and Pomphrey, and Chapman, Garrett, and Miller. © 1979 American Institute of Physics.
引用
收藏
页码:1862 / 1869
页数:8
相关论文
共 33 条
[1]   CALCULATING BOUND SPECTRUM BY PATH SUMMATION IN ACTION-ANGLE VARIABLES [J].
BERRY, MV ;
TABOR, M .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1977, 10 (03) :371-379
[2]   SEMICLASSICAL APPROXIMATIONS IN WAVE MECHANICS [J].
BERRY, MV ;
MOUNT, KE .
REPORTS ON PROGRESS IN PHYSICS, 1972, 35 (04) :315-+
[3]   CLOSED ORBITS AND REGULAR BOUND SPECTRUM [J].
BERRY, MV ;
TABOR, M .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1976, 349 (1656) :101-123
[4]  
BOGOLJUBOV N. N., 1976, METHODS ACCELERATED
[5]  
BORN M, 1960, MECHANICS ATOM
[6]   SEMICLASSICAL EIGENVALUES FOR NONSEPARABLE SYSTEMS - NONPERTURBATIVE SOLUTION OF HAMILTON-JACOBI EQUATION IN ACTION-ANGLE VARIABLES [J].
CHAPMAN, S ;
GARRETT, BC ;
MILLER, WH .
JOURNAL OF CHEMICAL PHYSICS, 1976, 64 (02) :502-509
[7]   SEMICLASSICAL CALCULATION OF ENERGY-LEVELS FOR NON-SEPARABLE SYSTEMS [J].
DELOS, JB ;
SWIMM, RT .
CHEMICAL PHYSICS LETTERS, 1977, 47 (01) :76-79
[8]  
EASTES W, 1974, J CHEM PHYS, V61, P502
[9]  
EINSTEIN A, 1917, VERHAND DEUT PHYS GE, V19, P82
[10]   THE STARK EFFECT FOR A RIGID ASYMMETRIC ROTOR [J].
GOLDEN, S ;
WILSON, EB .
JOURNAL OF CHEMICAL PHYSICS, 1948, 16 (07) :669-685