Application of the Brillouin--Loewdin perturbation expansion: lower bounds to the energy eigenvalues of the rigid rotator in an electric field

Journal Article · Wed Jun 01 04:00:00 EDT 1977 · Int. J. Quant. Chem.; (United States)

DOI:https://doi.org/10.1002/qua.560110606· OSTI ID:7142128

Grau, D

One of the variants of Lowdin's partitioning technique that makes use of a Brillouin-type perturbation expansion for the study of lower bounds to the eigenvalues of a Hamiltonian has not been applied to any practical quantum mechanical problem so far. To illustrate how powerful this method can be, an application is made to the rigid rotator in an electric field, which has already been studied by Choi and Smith using the bracketing function of an intermediate Hamiltonian. It turns out that for a given order of the basis set of the Bazley space the Brillouin--Lowdin perturbation expansion gives closer bounds than the method of Choi and Smith, except for the case l = m, where the procedures can be shown to be mathematically equivalent. Especially for high l--m the number of basis functions needed to attain the same accuracy is by far larger for the method of Choi and Smith than for the Brillouin--Lowdin method.

• Research Organization: Technical Univ., Vienna
• OSTI ID: 7142128
• Journal Information: Int. J. Quant. Chem.; (United States), Journal Name: Int. J. Quant. Chem.; (United States) Vol. 11:6; ISSN IJQCB
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
EIGENVALUES
ELECTRIC FIELDS
ENERGY DEPENDENCE
HAMILTONIANS
MATHEMATICAL OPERATORS
MECHANICS
MOTION
PERTURBATION THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
ROTATION
SERIES EXPANSION