Moment Method for Eigenvalues and Expectation Values

Blankenbecler, Richard; DeGrand, Thomas A.; Sugar, R.L.

doi:10.1103/PhysRevD.21.1055

Moment Method for Eigenvalues and Expectation Values

Richard Blankenbecler
(
- SLAC
)
,
Thomas A. DeGrand
(
- UC, Santa Barbara
)
,
R.L. Sugar
(
- UC, Santa Barbara
)

Sep, 1979

30 pages

Published in:

Phys.Rev.D 21 (1980) 1055

DOI:

10.1103/PhysRevD.21.1055

Report number:

SLAC-PUB-2404,
UCSB-TH-17-1979

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Abstract: (APS)

We present a simple technique for performing accurate calculations of the eigenvalues of quantum systems whose potential energy is a polynomial in the coordinates. The method involves the study of recursion relations between matrix elements of powers of the coordinate operator between the exact eigenstate and a conveniently chosen basis state. The general theory is developed and applied to three examples: the quartic oscillator, the octic oscillator, and two coupled quartic oscillators. Numerical results are given.

QUANTUM MECHANICS: ENERGY LEVELS
MODEL: OSCILLATOR
MATHEMATICAL METHODS: MOMENT
NUMERICAL CALCULATIONS

References(13)

Figures(0)

Moment Recursions and the Schrodinger Problem

John L. Richardson
(
- SLAC
)
,
Richard Blankenbecler
(
- SLAC
)

- Phys.Rev.D 19 (1979) 496-502
•
DOI:
- 10.1103/PhysRevD.19.496

- J.Chem.Phys. 57 1734

Transition Moments of Anharmonic Oscillators

K. Banerjee
(
- Indian Inst. Tech., Kanpur
)

- Phys.Lett.A 63 (1977) 223-224
•
DOI:
- 10.1016/0375-9601(77)90882-9

Anharmonic Oscillator Energies with Operator Recursion Mechanics

C.A. Uzes
(
- Georgia U.
)

- Phys.Rev.D 14 (1976) 3362-3370
•
DOI:
- 10.1103/PhysRevD.14.3362

Coupling constant analyticity for the anharmonic oscillator

B. Simon
(
- Princeton U.
)
,
A. Dicke
(
- Princeton U.
)

- Annals Phys. 58 (1970) 76-136
•
DOI:
- 10.1016/0003-4916(70)90240-X

Borel summability: Application to the anharmonic oscillator

- Phys.Lett.B 32 (1970) 631-634,
- In *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 240-243. (Phys. Lett. B32 (1970) 631-634). (see Book Index)
•
DOI:
- 10.1016/0370-2693(70)90564-2

Numerological Analysis of the WKB Approximation in Large Order

Carl M. Bender
(
- Washington U., St. Louis
)
,
K. Olaussen
(
- MIT, LNS
)
,
P.S. Wang
(
- MIT, LNS
)

- Phys.Rev.D 16 (1977) 1740-1748
•
DOI:
- 10.1103/PhysRevD.16.1740

Divergence of Perturbation Series and Pseudoparticles

L.N. Lipatov
(
- St. Petersburg, INP
)

- JETP Lett. 25 (1977) 104-107,
- Pisma Zh.Eksp.Teor.Fiz. 25 (1977) 116-119

Perturbation Theory at Large Order. 1. The phi**2N Interaction

E. Brezin
(
- Saclay
)
,
J.C. Le Guillou
(
- Paris U., VI-VII
)
,
Jean Zinn-Justin
(
- Saclay
)

- Phys.Rev.D 15 (1977) 1544-1557,
- Also in *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 91-104
•
DOI:
- 10.1103/PhysRevD.15.1544

Asymptotic Estimates in Perturbation Theory

G. Parisi
(
- IHES, Bures-sur-Yvette
)

- Phys.Lett.B 66 (1977) 167-169,
- Also in *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 112-114
•
DOI:
- 10.1016/0370-2693(77)90168-X

Perturbation Theory at Large Orders for Potential with Degenerate Minima

E. Brezin
(
- Saclay
)
,
G. Parisi
(
- IHES, Bures-sur-Yvette
)
,
Jean Zinn-Justin
(
- Saclay
)

- Phys.Rev.D 16 (1977) 408-412,
- In *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 170-174. (Phys. Rev. D16 (1977) 408-412) and Saclay CEN - D.PH.T-77-016 (77,rec.Apr.) 13 p. (see Book Index)
•
DOI:
- 10.1103/PhysRevD.16.408

Instanton Contributions to the Energy Spectrum of a One-Dimensional System

Eldad Gildener
(
- UC, San Diego
)
,
Adrian Patrascioiu
(
- UC, San Diego
)

- Phys.Rev.D 16 (1977) 423-430,
- Phys.Rev.D 16 (1977) 3616 (erratum)
•
DOI:
- 10.1103/PhysRevD.16.423

Nonlinear Contributions to the Partition Function of a Double Well Oscillator

Barry J. Harrington
(
- New Hampshire U.
)

- Phys.Rev.D 18 (1978) 2982
•
DOI:
- 10.1103/PhysRevD.18.2982