Bound states of the hydrogen atom in the presence of a magnetic monopole field and an Aharonov-Bohm potential (original) (raw)
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Journal of Mathematical Physics, 1995
In the present article we analyze the problem of a relativistic Dirac electron in the presence of a combination of a Coulomb eld, a 1=r scalar potential as well as a Dirac magnetic monopole and an Aharonov-Bohm potential. Using the algebraic method of separation of variables, the Dirac equation expressed in the local rotating diagonal gauge is completely separated in spherical coordinates, and exact solutions are obtained. We compute the energy spectrum and analyze how it depends on the intensity of the Aharonov-Bohm and the magnetic monopole strengths.
Exact solution for a hydrogen atom in a magnetic field of arbitrary strength
An exact solution describing the quantum states of a hydrogen atom in a homogeneous magnetic field of arbitrary strength is obtained in the form of a power series in the radial variable with coefficients being polynomials in the sine of the polar angle. Energy levels and wave functions for the ground state and for several excited states are calculated exactly for the magnetic field varying in the range 0ϽB/(m 2 e 3 c/ប 3 )р4000.
Physical Review D
Formulations of magnetic monopoles in a Hilbert-space formulation of quantum mechanics require Dirac's quantization condition of magnetic charge, which implies a large value that can easily be ruled out for elementary particles by standard atomic spectroscopy. However, an algebraic formulation of nonassociative quantum mechanics is mathematically consistent with fractional magnetic charges of small values. Here, spectral properties in nonassociative quantum mechanics are derived and applied to the ground state of hydrogen with a magnetically charged nucleus. The resulting energy leads to new strong upper bounds for the magnetic charge of various elementary particles that can appear as the nucleus of hydrogenlike atoms, such as the muon or the antiproton.
Chinese Physics B, 2018
We need to solve a suitable exponential form of the position-dependent mass (PDM) Schrödinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the influence of the external magnetic and Aharonov-Bohm (AB) flux fields. The bound state energies and their corresponding wave functions are calculated for spatiallydependent mass distribution function of a physical interest. A few plots of some numerical results to the energy are shown.
THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD
International Journal of Modern Physics E, 2006
In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the no magnetic field case analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n = 2 − 10 and m = 0 − 1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.
The quadratic Zeeman effect for highly excited hydrogen atoms in weak magnetic fields
Journal of Physics B: Atomic and Molecular Physics, 1984
The hydrogen Rydberg states in the presence of weak magnetic fields areanalytically investigated by using quantum mechanical first-order perturbation theory. The unperturbed hydrogenic wavefunctions, which diagonalise the quadratic Zeeman interaction within the subspace of states with fixed principal quantum number n, are obtained by separation of variables on the Fock hypersphere in momentum space. By considering n as a large parameter, the comparison equation method is employed to find the uniform asymptotics of eigenfunctions and asymptotic expansions of quadratic Zeeman energies corresponding to the outermost components of the Zeeman n manifold. The results obtained are compared with other theoretical predictions.
2019
Considering the stationary Schrödinger equation for a general pseudo-Coulomb potential as the normal form of the associated Laguerre equation, we review, in one and three dimensions, the bound-state solutions for the potential, when the inverse-square-term coupling is not less than a negative critical value. We show that, as a consequence of the inverse-square-term coupling being a two-to-one mapping for all but one of the allowed negative values of its parameter, an additional sequence of bound-state energies emerges for each of the respective potentials. In this framework, the slightest relaxation of the boundary condition for the radial wave function at the origin results in minus-infinity ground-state energy for the Coulomb potential, rendering the hydrogen atom unstable. The article has been published in the journal "New Horizons in Mathematical Physics", Vol. 3, No. 4, December 2019. Available at: https://dx.doi.org/10.22606/nhmp.2019.34001