A quantum mechanical curvature theorem

被引：20

作者：

Silverman, J. N. ^{[1
]}

Van Leuven, J. C. ^{[1
]}

机构：

[1] Battelle Inst, Ctr Adv Studies, Carouge, Switzerland

来源：

CHEMICAL PHYSICS LETTERS | 1970年 / 7卷 / 01期

关键词：

D O I：

10.1016/0009-2614(70)80242-1

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：

A general quantum mechanical curvature theorem of the form d(2)epsilon/d lambda(2) <= <psi vertical bar d(2)H/d lambda(2)vertical bar psi) is established by means of perturbational-variational theory; here, psi and epsilon are the exact eigenfunctions and eigenvalues of the Schrodinger time-independent equation, H is the Hamilton operator, and lambda is any real parameter occurring in H. The theorem is also established for arbitrary optimum variational solutions to the Schrodinger equation. Several applications of the curvature theorem are discussed in conjunction with perturbation theory and the stability of approximate wave functions.

引用

页码：37 / 42

页数：6

共 16 条

[1] BIRKHOFF G, 1958, SURVEY MODERN ALGEBR, P271
[2] Brown WB., 1958, P CAMBRIDGE PHIL SOC, V54, P251
[3] CONDON EU, 1957, THEORY ATOMIC SPECTR, P33
[4] COURANT R, 1947, DIFFERENTIAL INTEGRA, V2, P204
[5] NOTE ON PERTURBATION THEORY
EPSTEIN, ST
[J]. AMERICAN JOURNAL OF PHYSICS, 1954, 22 (09) : 613 - 614
[6] Forces in molecules
Feynman, RP
[J]. PHYSICAL REVIEW, 1939, 56 (04): : 340 - 343
[7] THE STABILITY OF A WAVEFUNCTION UNDER A PERTURBATION
HALL, GG
[J]. PHILOSOPHICAL MAGAZINE, 1961, 6 (62): : 249 - 258
[8] HEILMANN H, 1937, EINFUHRUNG QUANTENCH
[9] HIRSCHFELDER JO, 1964, ADV QUANTUM CHEM, V1, P255
[10] THE ELECTROSTATIC CALCULATION OF MOLECULAR ENERGIES .2. APPROXIMATE WAVE FUNCTIONS AND THE ELECTROSTATIC METHOD
HURLEY, AC
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1954, 226 (1165): : 179 - 192

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