The Energy Eigenvalues of the Two Dimensional Hydrogen Atom in a Magnetic Field

Abstract

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.

Anisotropic features of two-dimensional hydrogen atom in magnetic field

“…The algorithm given in Chapter 2 was used to calculate the ground state energy of the 2D hydrogen atom in the magnetic field perpendicular to the plane of electron motion. The obtained GSE values that were calculated by us using the infinite proton mass approximation and by other authors using the method of asymptotic iterations [19] and the variational approach [20] for different values of the magnetic field are shown in Table 3. The results are consistent with the results of other authors [19,20].…”

“…The influence of the external magnetic field, which is perpendicular to the plane of electron motion, on the spectrum of 2D hydrogen was investigated by means of a two-point Pade approximation [18], method of asymptotic iterations [19], variational approach [20,21], as well as analytically for individual values of the magnetic field [22]. Studies of hydrogen in strong magnetic fields [23][24][25] are associated with the astrophysical applications: the magnitude of the magnetic field in dwarf stars reaches 10 2 -10 5 T, whereas in neutron stars -10 7 -10 9 T [26].…”

“…The aim of the current work is the numerical investigation of the anisotropic properties of the twodimensional hydrogen atom induced by a magnetic field. In contrast to the previous works [18][19][20][21][22]25], we study the dependence of the spectrum and the wave functions of the system on arbitrary directions of the magnetic field forming an angle α with the normal to the plane of electron motion (see Fig. 1).…”

Bound-State Solution of s-Wave Klein-Gordon Equation for Woods-Saxon Potential

“…AIM has been used in many physical systems to obtain the corresponding eigenvalues and eigenfunctions [26][27][28][29][30][31]. Still, there are a few applications on KG equation with AIM [32][33][34] with a general transformation between vector and scalar potentials.…”

Two-dimensional electron states bound to an off-plane donor in a magnetic field

“…These studies have been motivated by the experimental realization of confined shallow donor impurities and excitons in quasi-2D quantum well structures. The energy levels and the orbitals [19,20] of the 2D hydrogen atom, the properties in magnetic fields [19,21], the dynamical symmetries [16][17][18], as well as the effects of the Rashba spinorbital coupling [22], have been studied. The investigation of the 2D electronic states bound to an off-plane donor in the presence of a magnetic field is strongly motivated by the technological development and, naturally, has become the next step forward.…”