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.

APPROXIMATE MOLECULAR ORBITALS: IV. THE 3dδg AND 4fδu STATES OF H2+

1967 ◽  
Vol 45 (8) ◽  
pp. 2533-2542 ◽  
Author(s):  
M. Cohen ◽  
R. P. McEachran ◽  
Sheila D. McPhee
Keyword(s):  
Perturbation Theory ◽  
Variational Methods ◽  
Excellent Agreement ◽  
Hydrogen Molecule ◽  
Wave Functions ◽  
Simple Criterion ◽  
Wide Range ◽  
Approximate Wave ◽  
Exact Calculations ◽  
Schrödinger Perturbation

Properties of the lowest even and odd δ states of the hydrogen molecule–ion have been calculated using approximate wave functions. These were derived using a combination of Rayleigh–Schrödinger perturbation theory and variational methods, which have been applied previously to calculate the corresponding wave functions of the lowest σ and π states. Our total molecular energies are in excellent agreement with the recent exact calculations of Hunter and Pritchard (1967). A simple criterion is suggested for judging the accuracy of the approximate orbitals, which indicates that all the molecular properties calculated will be accurate over a wide range of internuclear separations.

APPROXIMATE MOLECULAR ORBITALS: III. THE 1sσ AND 2pπ STATES OF HeH++

1967 ◽  
Vol 45 (7) ◽  
pp. 2231-2238 ◽  
Author(s):  
M. Cohen ◽  
R. P. McEachran ◽  
Sheila D. McPhee
Keyword(s):  
Perturbation Theory ◽  
Molecular Orbitals ◽  
Wave Functions ◽  
Variational Techniques ◽  
Approximate Wave ◽  
Schrödinger Perturbation

A combination of Rayleigh–Schrödinger perturbation theory and variational techniques, previously used to calculate the wave functions of the lowest σ and π states of H2+ has been applied to the 1sσ and 2pπ states of HeH++. The accuracy of the resulting approximate wave functions is demonstrated by comparing a number of quantities calculated with them with the corresponding exact values.

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.

The molecular orbital theory of chemical valency. III. Properties of molecular orbitals

1950 ◽  
Vol 202 (1069) ◽  
pp. 155-165 ◽  
Keyword(s):  
Perturbation Theory ◽  
Molecular Orbital ◽  
Molecular Orbitals ◽  
Molecular Properties ◽  
The Other ◽  
Molecular Orbital Theory ◽  
Special Significance ◽  
Orbital Theory ◽  
Molecular Systems ◽  
Normal States

The discussion of molecular orbitals and equivalent orbitals, given in previous papers, is carried a stage further. It is shown that certain molecular properties can be evaluated using either equivalent or molecular orbitals. On the other hand, a study of the changes produced by ionization demonstrates that molecular orbitals have a special significance and that certain energy parameters associated with them are closely related to ionization potentials. For the purpose of this discussion a perturbation theory is developed to deal with the changes produced in molecular systems when disturbed from their normal states.

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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