Variational-integral perturbation corrections of some lower excited states for hydrogen atoms in magnetic fields

Abstract

A variational-integral perturbation method (VIPM) is established by combining the variational perturbation with the integral perturbation. The first-order corrected wave functions are constructed, and the second-order energy corrections for the ground state and several lower excited states are calculated by applying the VIPM to the hydrogen atom in a strong uniform magnetic field. Our calculations demonstrated that the energy calculated by the VIPM only shows a negative value, which indicates that the VIPM method is more accurate than the other methods. Our study indicated that the VIPM can not only increase the accuracy of the results but also keep the convergence of the wave functions.

Variational-Integral Perturbation Corrections for Hydrogen Atoms in Magnetic Fields

“…𝜆 𝐸 (0) 𝑓 𝑝 𝐸𝑣𝑝 [28] Killingbeak [27] Praddaude [26] Kravchenko [29] [36] 1𝑠 Jason [28] −0.2498 −0.2472 −0.2335 −0.1916 −0.06715 Smith [24] −0.2498 −0.2472 −0.2340 −0.09785 Kravchenko [29] 0.2548 0.2672 0.2840 0.2961 0.2978 Yuan [36] − [29] 0.2549 0.2688 0.2928 0.3248 0.3703 Yuan [36] − A number of results have been obtained by studying the effect of a magnetic field on the spectrum of hydrogen. We construct the corrected wave functions and calculate the energy corrections for the ground state and some excited states by applying the VIPM to the hydrogen atom in a strong and uniform magnetic field.…”

“…In the present study, applying the improved Rayleigh-Schrödinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electrons as perturbations, [33,34] we employ the improved variational-perturbation method (VIPM) based on the integral equation to solve the heavy quarkonium in the 2𝑆 state. [35] We apply the VIPM to the hydrogen atom in a strong and uniform magnetic field, [36] construct corrected wave functions and calculate energy corrections for ground state and some excited states such as 4𝑑2, 4𝑑1, 4𝑑0, 4𝑑.1, 4𝑑.2, 4𝑓 3, 4𝑓 2, • • •. These values are compared with those of the elaborate calculations of Smith et al [10] and the simple basis variational calculations of Jason.…”

“…We only consider the nondegenerate cases of the hydrogen atom in a uniform magnetic field. For the simple case 𝑛 = 1, 𝑙 = 0, 𝑚 = 0 with 1 𝑆 states, the zeroth-order wave function 𝜑 (0) 100 (𝜆, 𝑟, 𝜃, 𝜙) is [36]…”

Ground-state energy of beryllium atom with parameter perturbation method

“…Perturbation theory is widely used for solving a Schrödinger equation that has no exact analytical solution. [1][2][3][4][5][6] It is well-known that the accuracy of the calculated energies from perturbation theory depends on the magnitude of the perturbation term in the Hamiltonian of the Schrödinger equation. Recently, Zhang et al [7,8] proposed a parameter perturbation method to minimize the influence of the perturbation term and this method gives a good estimate of the ground-state energy for the helium-like atom.…”