Error in an approximate wave function and an error minimization scheme

2003 ◽  
Vol 96 (5) ◽  
pp. 492-500 ◽  
Author(s):  
S. Mukhopadhyay ◽  
K. Bhattacharyya
Keyword(s):  
Wave Function ◽  
Error Minimization ◽  
Approximate Wave Function ◽  
Approximate Wave ◽  
Minimization Scheme

Electronic wave functions II. A calculation for the ground state of the beryllium atom

1950 ◽  
Vol 201 (1064) ◽  
pp. 125-137 ◽  
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Ground State ◽  
Accurate Result ◽  
Energy Criterion ◽  
Wave Functions ◽  
Exponential Functions ◽  
Approximate Wave Function ◽  
Electronic Wave Functions ◽  
Approximate Wave

An approximate wave function expressed in terms of exponential functions, spherical harmonics, etc., with numerical coefficients has been calculated for the ground state of the beryllium atom . Judged by the energy criterion this gives a more accurate result than the Hartree result which was the best previously known. This has been calculated as a trial of a fresh method of calculating atomic wave functions. A linear combination of Slater determinants is treated by the variational method. The results suggest that this will provide a more powerful and convenient method than has previously been available for atoms with more than two electrons.

Variational study on the ground state of the spin XY magnet

1978 ◽  
Vol 56 (7) ◽  
pp. 902-912 ◽  
Author(s):  
Masuo Suzuki ◽  
Seiji Miyashita
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Ground State ◽  
State Energy ◽  
Finite Lattice ◽  
Long Range Order ◽  
Lattice Method ◽  
Approximate Wave Function ◽  
Approximate Wave ◽  
Variational Study

An approximate wave function of the ground state of the spin [Formula: see text] XY magnet is derived using a variational method. This wave function yields estimates of the ground state energy and long-range order which agree very well with the results obtained by Betts and Oitmaa by a finite lattice method.

Hypervirial theorems and perturbation theory in quantum mechanics

1965 ◽  
Vol 283 (1393) ◽  
pp. 229-237 ◽  
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Wave Functions ◽  
First Order ◽  
Optimum Energy ◽  
Arbitrary Operator ◽  
Approximate Wave Function ◽  
Hypervirial Theorem ◽  
Variational Wave Functions ◽  
Approximate Wave

Previous ideas about the way in which hypervirial theorems might be used to improve approximate wave functions are discussed. To provide a firmer foundation for these ideas, a link is established between hypervirial theorems and perturbation theory. It is proved that if the first-order perturbation correction to the expectation value of an arbitrary operator vanishes, then the approximate wave function used satisfies a certain hypervirial theorem. Conversely, if an arbitrary hypervirial theorem is satisfied by the wave function, then it is proved that the expectation values of certain operators have vanishing first-order corrections. Some consequences of the theory as applied to variational wave functions with optimum energy are developed. The results are illustrated by the use of a simple approximate wave function for the ground state of the helium atom.

The molecular orbital theory of chemical valency XX. The energy in higher approximations

1955 ◽  
Vol 230 (1182) ◽  
pp. 424-428 ◽  
Keyword(s):  
Wave Function ◽  
Total Energy ◽  
Molecular Orbital ◽  
Molecular Orbital Theory ◽  
Bond Energies ◽  
Orbital Theory ◽  
Conjugated Molecules ◽  
Approximate Wave Function ◽  
Approximate Wave

The equations determining the optimum orbitals in a many-determinant approximate wave function are given and their relation to the total energy considered. As expected, the form of the energy shows that bond energies will be nearly additive in non-conjugated molecules as long as they are not strongly polar, but that this will not be so for conjugated molecules.

Two-dimensional approximate wave function for the three-body Coulomb problem

2000 ◽  
Vol 61 (5) ◽  
Author(s):  
S. Otranto ◽  
W. R. Cravero ◽  
G. Gasaneo ◽  
F. D. Colavecchia ◽  
C. R. Garibotti
Keyword(s):  
Wave Function ◽  
Two Dimensional ◽  
Coulomb Problem ◽  
Approximate Wave Function ◽  
Approximate Wave ◽  
Three Body

A remark on Moore's new method of obtaining approximate solutions of the Dirac equation

1979 ◽  
Vol 57 (12) ◽  
pp. 2114-2119 ◽  
Author(s):  
Yasuo Tomishima
Keyword(s):  
Exact Solution ◽  
Wave Function ◽  
Approximate Solution ◽  
Dirac Equation ◽  
Approximate Solutions ◽  
Zero Order ◽  
New Method ◽  
Hydrogenic Atom ◽  
Approximate Wave Function ◽  
Approximate Wave

The new method for obtaining an approximate solution of the Dirac equation proposed by Moore is applied rigorously in zero order to the hydrogenic atom, and the results are compared with the exact solution and with those obtained by Pauli's approximation. It is concluded that up to the order of α2 the three methods give the same energy values, but the higher order contribution included in Moore's method makes the energy worse than Pauli's. Moore's zeroth approximate wave function is also examined.

scholarly journals Superradiation of Dirac particles in KN ds black hole

2021 ◽  
Author(s):  
Wen-Xiang Chen
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
Potential Barrier ◽  
Imaginary Part ◽  
Dirac Particle ◽  
Field Of View ◽  
Dirac Particles ◽  
Maximum Value ◽  
Approximate Wave Function ◽  
Approximate Wave

In this article, we process the approximate wave function of the Dirac particle outside the horizon of the KN ds black hole to obtain V, and then derive V (including real and imaginary parts). We deal with the real and imaginary parts separately. When V (real part or imaginary part) has a maximum value, there may be a potential barrier outside the field of view to have a chance to produce superradiation.

scholarly journals Origin Invariant Optical Rotation in the Length Dipole Gauge without London Atomic Orbitals

2020 ◽  
Author(s):  
Marco Caricato
Keyword(s):  
Density Functional ◽  
Optical Rotation ◽  
Center Of Mass ◽  
Density Functional Method ◽  
Functional Method ◽  
Coupled Cluster ◽  
Atomic Orbitals ◽  
Numerical Tests ◽  
Approximate Wave Function ◽  
Approximate Wave

<div> <div> <div> <p>We present an approach to perform origin-invariant optical rotation calculations in the length dipole gauge without recourse to London atomic orbitals, called LG(OI). The LG(OI) approach works with any approximate wave function or density functional method, but here we focus on the implementation with the coupled cluster (CC) with single and double excitations method because of the lack of production-level alternatives. Preliminary numerical tests show the efficacy of the LG(OI) procedure, and indicate that conventional CC-LG calculations with the origin in the center of mass of a molecule may still carry significant origin dependence. </p> </div> </div> </div>

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