Quadratic Zeeman effect for hydrogen: A method for rigorous bound-state error estimates

Fonte, G.; Falsaperla, Paolo; Schiffrer, G.; Stanzial, Domenico

doi:10.1103/physreva.41.5807

Cited by 43 publications

(31 citation statements)

References 21 publications

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“…4A it can be observed that, for strong magnetic fields, the binding energy reaches a constant value for large QWW radii. The results in the large R limit and for magnetic fields in the experimental range (g ≤ 2), [8,14] are compared with the hydrogenic atom limit [16]. In Fig.…”

Section: Resultsmentioning

confidence: 98%

Magnetic field dependence of the binding energy of shallow donors in GaAs quantum-well wires

Niculescu

Gearba

Cone

et al. 2001

Superlattices and Microstructures

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Section: Resultsmentioning

confidence: 98%

Magnetic field dependence of the binding energy of shallow donors in GaAs quantum-well wires

Niculescu

Gearba

Cone

et al. 2001

Superlattices and Microstructures

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“…(We do not use kinetic balance [19] here, but plan to apply it to the case of finite [10]. Reference [7].…”

Section: A Variational Methodsmentioning

confidence: 99%

“…When Z = 0, the solution of the Dirac equation can be obtained by considering [22] the square of the Hamilto- [10]. Reference [7].…”

Section: A Variational Methodsmentioning

confidence: 99%

“…Many nonrelativistic methods have been used [4 -10], including the variational method [4,6], Hartree-Fock approach [7], finite-element method [8], and bounds by eigenvalue-moment method [9] and by I&ato's method [10]. With the increasing accuracy of the nonrelativistic calculations of hydrogenic atoms in intense magnetic fields [6 -10], relativistic corrections become necessary.…”

Section: Introductionmentioning

confidence: 99%

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Relativistic and nonrelativistic finite-basis-set calculations of low-lying levels of hydrogenic atoms in intense magnetic fields

Chen

Goldman

1992

Phys. Rev. A

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A finite-basis-set method is used to calculate relativistic and nonrelativistic binding energies of an electron in a static Coulomb field and in magnetic fields of arbitrary strength (0 ( B & 10 G).The basis set is composed of products of Slaterand Landau-type functions, and it contains the exact solutions at both the Coulomb limit (B = 0) and the Landau limit (Z = 0). Relativistic variational collapse is avoided and highly accurate results are obtained with the basis set. The relativistic corrections obtained for intense magnetic fields (B + 10 G) differ from the previous relativistic calculations based on the adiabatic approximations.It is found that the sign of the relativistic correction changes from negative to positive near B 10 ' 0 for the ground state and near B 10 G for the 2psyz(ti = -3/2) excited state of hydrogen. The method is checked to be very accurate by means of the virial theorem, sum rules, and the relativistic low-B limit where comparison can be made with perturbation results. In the nonrelativistic limit of the Dirac equation, our results agree with other accurate nonrelativistic calculations available and with our own calculations based on the Schrodinger equation, which converge to more significant digits than previous calculations for the whole range of magnetic fields.PACS number(s): 32.60.+i, 31.30.Jv, 31.10.+z

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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%

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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Quadratic Zeeman effect for hydrogen: A method for rigorous bound-state error estimates

Cited by 43 publications

References 21 publications

Magnetic field dependence of the binding energy of shallow donors in GaAs quantum-well wires

Magnetic field dependence of the binding energy of shallow donors in GaAs quantum-well wires

Relativistic and nonrelativistic finite-basis-set calculations of low-lying levels of hydrogenic atoms in intense magnetic fields

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

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