APPROXIMATE MOLECULAR ORBITALS: I. THE 1sơg AND 2pơu STATES OF H2+

1966 ◽  
Vol 44 (11) ◽  
pp. 2809-2825 ◽  
Author(s):  
M. Cohen ◽  
R. P. McEachran
Keyword(s):  
Perturbation Theory ◽  
Molecular Orbitals ◽  
Wave Functions

Simple analytic representations of the wave functions of the lowest even and odd σ states of H2+ have been obtained using perturbation theory. Their accuracy is demonstrated by comparing the values of a number of molecular quantities computed using the approximate functions with the corresponding exact values.

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.

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.

The direct calculation of the first-order density matrix for atoms

1965 ◽  
Vol 283 (1393) ◽  
pp. 194-202 ◽  
Keyword(s):  
Perturbation Theory ◽  
Density Matrix ◽  
Ground State ◽  
Direct Calculation ◽  
Molecular Orbitals ◽  
Natural Orbitals ◽  
Mean Values ◽  
First Order ◽  
Order Contribution

The theory of isoelectronic sequences of atoms has been developed as a perturbation theory and is extended here to the calculation of the first-order density matrix. It is shown that the calculation of the first-order contribution to this matrix can be reduced to the solution of a number of one-electron equations. These equations have been solved for the helium ground state, the helium 3 S state and the lithium ground state. From the density matrix, mean values of one-electron operators can be derived by integration. A variety of these mean values is quoted and the significance of the stable values discussed. From the density matrix the natural orbitals can be derived and these are found to be identical with the unrestricted molecular orbitals to terms of zero and first order.

The Polarizability of Molecular Hydrogen H2

1936 ◽  
Vol 32 (2) ◽  
pp. 260-264 ◽  
Author(s):  
C. E. Easthope
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Molecular Hydrogen ◽  
Applied Field ◽  
Minimum Energy ◽  
Wave Functions ◽  
The Other ◽  
System A ◽  
The One ◽  
Two Parameter

1. The problem of calculating the polarizability of molecular hydrogen has recently been considered by a number of investigators. Steensholt and Hirschfelder use the variational method developed by Hylleras and Hassé. For ψ0, the wave function of the unperturbed molecule when no external field is present, they take either the Rosent or the Wang wave function, while the wave functions of the perturbed molecule were considered in both the one-parameter form, ψ0 [1+A(q1 + q2)] and the two-parameter form, ψ0 [1+A(q1 + q2) + B(r1q1 + r2q2)], where A and B are parameters to be varied so as to give the system a minimum energy, q1 and q2 are the coordinates of the electrons 1 and 2 in the direction of the applied field as measured from the centre of the molecule, and r1 and r2 are their respective distances from the same point. Mrowka, on the other hand, employs a method based on the usual perturbation theory. Their numerical results are given in the following table.

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