Explicit Formulas inDegenerateRayleigh-Schrödinger Perturbation Theory for the Energy and Wave Function, Based on a Formula of Lagrange

1971 ◽  
Vol 4 (6) ◽  
pp. 2191-2199 ◽  
Author(s):  
Harris J. Silverstone ◽  
Thomas T. Holloway
Keyword(s):  
Wave Function ◽  
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.

APPROXIMATE MOLECULAR ORBITALS: V. THE 3dδ STATE OF HeH++

1967 ◽  
Vol 45 (8) ◽  
pp. 2749-2754 ◽  
Author(s):  
M. Cohen ◽  
R. P. McEachran ◽  
Sheila D. McPhee
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Variational Methods ◽  
High Accuracy ◽  
Molecular Orbitals ◽  
Molecular Properties ◽  
Simple Criterion ◽  
Molecular Wave Function ◽  
Schrödinger Perturbation

The techniques of Rayleigh–Schrödinger perturbation theory and variational methods have been used to obtain an approximate molecular wave function for the lowest δ state of the HeH++ ion. Its accuracy may be judged by a simple criterion proposed in an earlier paper, and molecular properties computed using it should have high accuracy. The main conclusions of this series of papers are reviewed briefly.

scholarly journals Energy and Wave function Analysis on Harmonic Oscillator Under Simultaneous Non-Hermitian Transformations of Co-ordinate and Momentum: Iso-spectral case

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 492-497
Author(s):  
Biswanath Rath ◽  
P. Mallick
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Harmonic Oscillator ◽  
Function Analysis ◽  
Energy Eigenvalue ◽  
Algebraic Approach ◽  
Wave Function Analysis ◽  
Wavefunction Analysis

AbstractWe present a complete energy and wavefunction analysis of a Harmonic oscillator with simultaneous non-hermitian transformations of co-ordinate $(x \rightarrow \frac{(x + i\lambda p)}{\sqrt{(1+\beta \lambda)}})$ and momentum $(p \rightarrow \frac {(p+i\beta x)}{\sqrt{(1+\beta \lambda)}})$ using perturbation theory under iso-spectral conditions. We observe that two different frequencies of oscillation (w1, w2)correspond to the same energy eigenvalue, - which can also be verified using a Lie algebraic approach.

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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