On the application of extended precision arithmetic to quantum mechanical calculations

Kravchenko, Yu. P.; Liberman, Michael A.

doi:10.1002/(sici)1097-461x(1997)62:6<593::aid-qua3>3.0.co;2-r

Cited by 9 publications

(3 citation statements)

References 27 publications

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“…For the calculation of the low-lying states of a hydrogen atom in an ultra-high magnetic field (10 5 −10 9 T), which is the case for atoms in the atmosphere of white dwarfs and neutron stars, existent effective methods includes basis set method using different basis functions [3][4][5][6][7][8], eigenvalue analysis method [9][10][11], finite element method [12], adiabatic approximate method [13][14][15], and series method [16][17][18]. Among these methods, the series method introduced by Kravchenko and Liberman give the most accurate results for the low-lying spectra of hydrogen atom in a magnetic field [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…Among these methods, the series method introduced by Kravchenko and Liberman give the most accurate results for the low-lying spectra of hydrogen atom in a magnetic field [16][17][18]. The disadvantage of this method is its requirement for high computational precision up to 280 decimal digits, which is not available in common computers [16].…”

Section: Introductionmentioning

confidence: 99%

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Hydrogen atom in strong magnetic field: A high accurate calculation in spheroidal coordinates

et al. 2006

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A B-spline-type basis set method for the calculation of hydrogen atom in strong magnetic fields in the frame of spheroidal coordinates has been introduced. High accurate energy levels of hydrogen in the magnetic field, with strength ranging from 0 to 1000 a.u., have been obtained. For the ground state, 1s 0 , energies with at least 11 significant digits have been obtained. For the low-lying excited state, 2 p −1 , energies with at least 9 significant digits are obtained. The method has also been applied to the calculation of hydrogen Rydberg states in laboratory magnetic fields. Energy spectra with at least 10 significant digits are presented. A comparison with other results in the literatures has been performed. Our results are comparable to the most accurate one up to date. A possible extension to the cases of parallel and crossed electric and magnetic fields have been discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hydrogen atom in strong magnetic field: A high accurate calculation in spheroidal coordinates

et al. 2006

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“…In the nonrelativistic quantum mechanics the problem of the hydrogenic atom in a homogeneous magnetic field can be solved exactly, in a sense that energy and the wavefunction can be computed with any precision, in the form of power series in the radial variable with coefficients being polynomials in the sine of the polar angle [10,11,12]. Terms in the series are connected by explicit recurrent relations and a set of mathematical solutions is generated by starting from appropriately chosen starting values.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Relativistic Hydrogenic Atom in Static and Uniform Magnetic Field

Rutkowski

Poszwa

2005

Phys. Scr.

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The solution of the Dirac equation for hydrogenic atom in static and uniform magnetic field is obtained in the full four-component form. In a basis of spherical spinors wavefunctions for bound states as linear combinations of exact particular solutions in the form of power series are determined by imposing on every radial function the boundary exponential decay. The accuracy of the ground state energy for low and moderately strong magnetic fields exceeds that of previous fully relativistic calculations. In the limit of low magnetic field the high accurate values of the relativistic energy are used to determine the relativistic corrections to the magnetizability up to 15th order in Z2/c2.

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Application of Gaussian-type basis sets to ab initio calculations in strong magnetic fields

Kravchenko

Liberman

1997

Int. J. Quant. Chem.

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ABSTRACT:It is shown that systematically constructed Gaussian-type basis sets applied to simplest one-electron systems in magnetic field varying from 0 to 2 X 108 T can reliably provide accuracy hartrees and better. Important features of the considered type of basis sets are absence of variational parameters and possibility to approach completeness in a controlled systematic manner. Methods of construction of such basis sets, outlined in the study, are of importance of future work on atomic and molecular calculations in strong magnetic fields. 0

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On the application of extended precision arithmetic to quantum mechanical calculations

Cited by 9 publications

References 27 publications

Hydrogen atom in strong magnetic field: A high accurate calculation in spheroidal coordinates

Hydrogen atom in strong magnetic field: A high accurate calculation in spheroidal coordinates

Analytical Solution for Relativistic Hydrogenic Atom in Static and Uniform Magnetic Field

Application of Gaussian-type basis sets to ab initio calculations in strong magnetic fields

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