Effective utilization of off-diagonal hypervirial relations considering diagonal hypervirial relation: harmonic oscillator case

Journal Article · Sat Dec 01 04:00:00 EST 1979 · Int. J. Quant. Chem.; (United States)

DOI:https://doi.org/10.1002/qua.560160614· OSTI ID:6917309

Sakamoto, K ^[1]; Terasaka, T

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1. Univ. of Electro-Communications, Tokyo, Japan

The effective utilization of hypervirial relations is scrutinized to improve the approximate excited-state functions in the harmonic oscillator system. A new method is presented that simultaneously employs the off-diagonal hypervirial relations with the diagonal hypervirial relation. In order to use these relations effectively, the following points are pointed out: the presented method is useful to get better reasonable results for the excitation energies and the state functions; the ground state given must satisfy the virial theorem; in the hypervirial operator used here as x/sup m/, the smaller integers of m's present better results; and the employment of the comparatively small number of trial basis functions of the type exp (-..gamma..x) is sufficient for reproducing the exact excited state. Especially among them, the second condition plays an important role. Applying all the proposals to the first and the second excited states, one gets a highly improved excitation energy, state function, and other physical quantities (e.g., transition moment and oscillator strength). The presented method is also found to be more effective than the employment of only the off-diagonal hypervirial relations or the method of the scaling operation. 2 figures, 4 tables.

• OSTI ID: 6917309
• Journal Information: Int. J. Quant. Chem.; (United States), Journal Name: Int. J. Quant. Chem.; (United States) Vol. 16:6; ISSN IJQCB
• Country of Publication: United States
• Language: English

Related Subjects

640305* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Theory-- (-1987)
74 ATOMIC AND MOLECULAR PHYSICS
DATA
ELECTRONIC EQUIPMENT
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EQUIPMENT
EXCITED STATES
FUNCTIONS
HARMONIC OSCILLATORS
INFORMATION
MATRIX ELEMENTS
NUMERICAL DATA
OSCILLATOR STRENGTHS
OSCILLATORS
THEORETICAL DATA
VIRIAL THEOREM
WAVE FUNCTIONS