Explicit Formulas for the Nth‐Order Wavefunction and Energy in Nondegenerate Rayleigh–Schrödinger Perturbation Theory

1970 ◽  
Vol 52 (3) ◽  
pp. 1472-1475 ◽  
Author(s):  
Harris J. Silverstone ◽  
Thomas T. Holloway
Keyword(s):  
Perturbation Theory ◽  
Explicit Formulas ◽  
Schrödinger Perturbation

Correlation energy in triplet electronic states. Application of the many-body Rayleigh-Schrödinger perturbation theory in the restricted Roothaan-Hartree-Fock formalism

1981 ◽  
Vol 46 (6) ◽  
pp. 1324-1331 ◽  
Author(s):  
Petr Čársky ◽  
Ivan Hubač
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Correlation Energy ◽  
Electronic States ◽  
Many Body ◽  
Third Order ◽  
Explicit Formulas ◽  
Hartree Fock ◽  
The Many ◽  
Schrödinger Perturbation

Explicit formulas over orbitals are given for the correlation energy in triplet electronic states of atoms and molecules. The formulas were obtained by means of the diagrammatic many-body Rayleigh-Schrodinger perturbation theory through third order assuming a single determinant restricted Roothaan-Hartree-Fock wave function. A numerical example is presented for the NH molecule.

Applicability of the schrödinger perturbation theory to bound states

1964 ◽  
Vol 10 (1) ◽  
pp. 73 ◽  
Author(s):  
K. Hausmann ◽  
W. Macke ◽  
P. Ziesche
Keyword(s):  
Perturbation Theory ◽  
Bound States ◽  
Schrödinger Perturbation

scholarly journals Quantum square-well with logarithmic central spike

2018 ◽  
Vol 33 (02) ◽  
pp. 1850009 ◽  
Author(s):  
Miloslav Znojil ◽  
Iveta Semorádová
Keyword(s):  
Perturbation Theory ◽  
Boundary Conditions ◽  
Closed Form ◽  
Wave Functions ◽  
Change Of Variables ◽  
State Dependent ◽  
Square Well ◽  
Strength Formula ◽  
Schrödinger Perturbation ◽  
Dependent Interaction

Singular repulsive barrier [Formula: see text] inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction [Formula: see text] in nonlinear Schrödinger equation. In the linearized case, Rayleigh–Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small [Formula: see text] or after an amendment of the unperturbed Hamiltonian. At any spike strength [Formula: see text], the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables [Formula: see text] which interchanges the roles of the asymptotic and central boundary conditions.

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