Ground and first excited states of excitons in a magnetic field

Cabib, Dario; Fabri, E.; Fiorio, G.

doi:10.1007/bf02911419

Cited by 172 publications

(21 citation statements)

References 13 publications

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“…5 Our analysis is relevant because prior results have been unsatisfactory in defining a convincing theory. Indeed, an assortment of approximate techniques have been used including variational methods, 6 Pade resummation analysis, 7 numerical integration, 8 order-dependent conformal transformations, 9 and virialtheorem Hellman-Feynman analysis. 10 Despite these efforts, the significant variation in ground-state-energy estimates, as cited in Table I, led to little confidence in ascertaining the correct theory.…”

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confidence: 99%

Rapidly Converging Bounds for the Ground-State Energy of Hydrogenic Atoms in Superstrong Magnetic Fields

et al. 1988

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The calculation of rapidly converging lower and upper bounds to the ground-state energy, E g , of hydrogenic atoms in superstrong magnetic fields (B^\0 9 G) has been an important theoretical problem for the past twenty-five years. Much effort has gone into reconciling the many different estimates for E g predicted by an assortment of techniques. On the basis of recently developed eigenvalue moment methods, a precise solution involving rapidly converging bounds to E g , for arbitrary superstrong magnetic field strengths, is now possible.

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confidence: 99%

Rapidly Converging Bounds for the Ground-State Energy of Hydrogenic Atoms in Superstrong Magnetic Fields

et al. 1988

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“…If E*(2) is to yield the exact energy when ~. = 0 it will happen that C2/A=2/rl 2, n=n~+l+ l, (19) where n, n r and I are the principal, radial and angular quantum numbers respectively and A =(A~/2 All2 ~_ A1/2~2 +~-2 -~-3 J. Equation (19), which follows immediately from E*(0)=-l/2n 2 and (12) and (13), poses a relation among A, C and n. The constant C is obtained at once from (17) and (18) c = (l/r) (r2> 1/2(,~ = 0) = {5n 2 q-1 --31(I + 1)} 1/2/21/2 n. (20) On the other hand, the well-known equality [29] …”

Section: The Methodsmentioning

confidence: 99%

“…In this article we develop a simple variational method based on the Heisenberg uncertainty relations that yields accurate enough estimations of the eigenvalues of the abovementioned model as well as of some expectation values. As will be seen later on, this procedure, which from now on will be called variational functional method (VFM), does not require a trial function and, so, it differs markedly from the usual variational approach [1,[7][8][9][10][11][12][13][14][15][16][17][18][19]. In * To whom correspondence should be addressed addition to this, the VFM is reminiscent of those semMassical approximations [20][21][22][23][24][25][26] which have been very useful to explain the spectra of Rydberg atoms in the zerofield ionization limit [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

A new variational approach to the hydrogen atom in magnetic fields

1984

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“…Recent astrophysical evidence indicates the existence of intense magnetic fields B of the order of 1018 G (1 G = 10-i T, tesla) on pulsars (1), and in this connection* the behavior of atoms has been discussed theoretically (2)(3)(4)(5)(6)(7)(8)(9)(10)(11). From the atomic physics viewpoint these intense magnetic fields provide a new atomic regime in which the magnetic interaction dominates the Coulomb interaction.…”

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Atomic Regime in Which the Magnetic Interaction Dominates the Coulomb Interaction for Highly Excited States of Hydrogen

Mueller¹,

Hughes²

1974

Proc. Natl. Acad. Sci. U.S.A.

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The atomic regime in which the interaction of the electron with an external magnetic field dominates the Coulomb interaction with the nucleus, relevant to pulsars, can be realized at laboratory magnetic fields for discrete autoionized states of hydrogen, at energies above the ionization limit. Approximate wave functions, energy levels, and electric dipole transition probabilities are presented for hydrogen, and an atomic beam absorption spectroscopy experiment at 50 kG is proposed to study this new regime.Recent astrophysical evidence indicates the existence of intense magnetic fields B of the order of 1018 G (1 G = 10-i T, tesla) on pulsars (1), and in this connection* the behavior of atoms has been discussed theoretically (2-11). From the atomic physics viewpoint these intense magnetic fields provide a new atomic regime in which the magnetic interaction dominates the Coulomb interaction. For example, the energy spectrum of hydrogen in an intense magnetic field is that of an electron in the magnetic field perturbed by the relatively small Coulomb interaction. This regime is achieved for the ground state of hydrogen for B of order 5 X 109 G, at which value the cyclotron radius is less than the Bohr radius. It would be interesting to study this new atomic regime in the laboratory. At any value of the magnetic field this regime is realized, e.g., for hydrogen, in a state of sufficiently high excitation (12-17).The nonrelativistic Schrbdinger equation for the relative motion of a hydrogen-like atom or ion in a uniform magnetic field taken along the z axis is approximately (18) For the intense magnetic field regime, the well known adiabatic approach, described initially by Schiff and Snyder (13), is applicable in which the fast motion in the plane perpendicular to the z-direction is considered separable from the relatively slow z-motion and the Coulomb interaction is neglected with regard to the perpendicular motion. The normalized eigenfunctions for the perpendicular motion of the electron in the magnetic field are (19)4'nm~pq')= 2irrc2( !+fl)! X (2 2) Llmm(p//2r22)eiO [2] in which r, -(hc/eB)'/2 is the cyclotron radius, L}'1 is the generalized Laguerre polynomial, n, = 0,1,2..., and m= 0, 4 1, -+2,.... The corresponding infinitely degenerate eigenenergies are E(°pm = (hwc/2)(2n, + JmJ + m + 1).Solutions of Eq. 1 are obtained in the formSubstitution of 4 into Eq. 1, multiplication by *pm* and integration over the p, 0 variables leads to a one-dimensional Schr6dinger equation for! P + Vn ImI(Z)jf(Z) = ef(z), [5] in which Vnpiml(Z) = -Ze2ffIcZn,,om(pO)j2(p2 + Z2) -'1/2pdpdo. [6] The discrete eigenfunctions and eigenenergies of Eq. 5 are written as fnpmna (z) and 5npmn5 where n, = 0,1,2,. orders the solutions of Eq. 5 in increasing energy and z nodes. They are infinite in number since asymptotically the leading term in Vnplml approaches -Ze2/z. There is also a continuum of solutions of Eq. 5 for e > 0, for unbounded motion along z. The discrete energy eigenvalues of Eq. 1 in the intense magnetic field regime ...

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Ground and first excited states of excitons in a magnetic field

Cited by 172 publications

References 13 publications

Rapidly Converging Bounds for the Ground-State Energy of Hydrogenic Atoms in Superstrong Magnetic Fields

Rapidly Converging Bounds for the Ground-State Energy of Hydrogenic Atoms in Superstrong Magnetic Fields

A new variational approach to the hydrogen atom in magnetic fields

Atomic Regime in Which the Magnetic Interaction Dominates the Coulomb Interaction for Highly Excited States of Hydrogen

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