Studies in Perturbation Theory. X. Lower Bounds to Energy Eigenvalues in Perturbation-Theory Ground State

1965 ◽  
Vol 139 (2A) ◽  
pp. A357-A372 ◽  
Author(s):  
Per-Olov Löwdin
Keyword(s):  
Perturbation Theory ◽  
Lower Bounds ◽  
Ground State ◽  
Energy Eigenvalues ◽  
Theory X

van der Waals perturbation theory for fermion and boson ground-state matter

1987 ◽  
Vol 35 (9) ◽  
pp. 3901-3910 ◽  
Author(s):  
V. C. Aguilera-Navarro ◽  
R. Guardiola ◽  
C. Keller ◽  
M. de Llano ◽  
M. Popovic ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Ground State ◽  
Van Der Waals

Calculation of energy eigenvalues via supersymmetric quantum mechanics

1989 ◽  
Vol 67 (10) ◽  
pp. 931-934 ◽  
Author(s):  
Francisco M. Fernández ◽  
Q. Ma ◽  
D. J. DeSmet ◽  
R. H. Tipping
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Potential Energy Function ◽  
Supersymmetric Quantum Mechanics ◽  
Energy Eigenvalues ◽  
Arbitrary Power ◽  
Rational Function Approximation ◽  
Ricatti Equation ◽  
Original Potential ◽  
Ground State Energies

A systematic procedure using supersymmetric quantum mechanics is presented for calculating the energy eigenvalues of the Schrödinger equation. Starting from the Hamiltonian for a given potential-energy function, a sequence of supersymmetric partners is derived such that the ground-state energy of the kth one corresponds to the kth eigen energy of the original potential. Various theoretical procedures for obtaining ground-state energies, including a method involving a rational-function approximation for the solution of the Ricatti equation that is outlined in the present paper, can then be applied. Illustrative numerical results for two one-dimensional parity-invariant model potentials are given, and the results of the present procedure are compared with those obtainable via other methods. Generalizations of the method for arbitrary power-law potentials and for radial problems are discussed briefly.

Solution of the Dirac Equation for the Rectilinear Periodic Motion of an Electron

1969 ◽  
Vol 24 (3) ◽  
pp. 344-349
Author(s):  
A. D. Jannussis
Keyword(s):  
Perturbation Theory ◽  
Dirac Equation ◽  
Periodic Motion ◽  
Periodic Potential ◽  
Bragg Reflection ◽  
Wave Number ◽  
Periodic Functions ◽  
Energy Bands ◽  
Energy Eigenvalues ◽  
The Hill

AbstractIn this paper the Dirac equation for a rectilinear onedimensional periodic potential is treated. It is shown that the energy eigenvalues are periodic functions of the wave number Kϰ and the continuous spectrum is split into energy bands. The end points of the energy bands are the points where the Bragg reflection takes place. These results are obtained by perturbation theory, as well as by the method of determinants, since the resulting eigenvalue equation has the form of a determinant which is similar to the Hill determinant.

Lower Bounds to Energy Eigenvalues

1969 ◽  
Vol 50 (8) ◽  
pp. 3339-3342 ◽  
Author(s):  
Alexander Mazziotti
Keyword(s):  
Lower Bounds ◽  
Energy Eigenvalues
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