Spectra of electron pair under harmonic and Debye potential

Abstract

Two electron systems confined by harmonic potential is known as harmonium. Such a system has been studied for many reasons in the literature. In this work we study harmonium under Debye potential. We use higher order finite difference method for the solution of Schrodinger equation. Complete energy spectrum of harmonium and harmonium under Debye potential is studied. Debye screening length shows considerable effect on the energy levels and the radial matrix elements. The results are analysed in the light of existing results and the comparison with available results shows remarkable agreement. KEYWORDSconfined harmonium, Debye potential, radial matrix element INTRODUCTIONThe study of confined atoms was initiated by Michels et al. [1] in 1937 in order to study the effect of high pressure on atomic hydrogen. Since then much of the work has been devoted to study confined atoms. Confined quantum systems have attracted many studies owing to their importance in the physics of quantum heterostructures, where, off late, many new structures are being proposed. [2][3][4][5][6][7] A few structures in various environments are studied using approximate potentials such as power series potentials and screened coulomb Debye potential. [8] The confinement and atoms under confinement have been studied in various interdisciplinary studies. [9][10][11][12][13][14][15][16][17] The study of such systems has gained importance because of technological importance of atoms, molecules, and ions in cavity and excitons in semiconductor heterostructures. [18,19] In addition, it is also a very well-known fact that the chemical reactivity of confined systems shows drastic change with change of confinement, hence it has led to many applications. Even atoms with high atomic numbers have been studied in different confinements. Jiao et al. [20] studied spectral and structural data of He atom under screened coulomb potential. Ghoshal and Ho [21] studied the ground state of two-electron system in generalized screened potential. Jiang et al. [22] studied this system under Lorentzian astrophysical plasma. Two interacting electrons with or without harmonic potential form a system that attracts a lot of interest. Two interacting electron system is a model system which is used to explore the physical aspects of many phenomena involving several electron systems. Two electrons confined in an infinite spherical well has been well studied theoretically. [23][24][25][26][27][28] Study of harmonium atom can be helpful in density functional theory and to study the optical properties of two-electron quantum dot. Even harmonium atom with more than two electrons [29][30][31][32] is also well studied in the literature due to its usefulness in solid state physics and quantum chemistry. Here, we study in detail the properties of harmonium in Debye environment. We solve this problem using eighth order finite difference method to describe the relative motion of the system. The effectiveness of our method is shown by comparing our results with those of available data for ...

Energy spectra of three‐dimensional harmonium under Debye potential obtained using the shifted 1/N expansion approach

“…The results of this article were verified with the previous results. In Table , the results of this article are compared to the values calculated by Munjal and Prasad . The present results show reasonable agreement with the previous results .…”

“…The results of present work were compared to the previous results to verify the accuracy of the shifted 1/N expansion method in calculating energies of harmonium. The results are in reasonable agreement, quantitatively and qualitatively, with those obtained using other different methods . At a high screening effect ( λ D → 0), harmonium atoms may be regarded as systems of independent harmonic oscillators and the single‐electron states are important.…”

“…It is simple and gives accurate eigenvalues without dealing with wave function of particles. The properties of the energy spectrum of harmonium under Debye potential were analysed using the eighth order finite difference method for the solution of Schrodinger equation . Debye screening length shows a considerable effect on the energy levels and the radial matrix elements …”

“…The properties of the energy spectrum of harmonium under Debye potential were analysed using the eighth order finite difference method for the solution of Schrodinger equation. [17] Debye screening length shows a considerable effect on the energy levels and the radial matrix elements. [17] In the shifted 1/N expansion, the calculations are carried out for states with arbitrary quantum numbers (the principal and orbital quantum numbers n and , respectively) using forth-order perturbation theory in the shifted expansion parameter 1∕k, where k = N + 2 − a.…”

“…[17] Debye screening length shows a considerable effect on the energy levels and the radial matrix elements. [17] In the shifted 1/N expansion, the calculations are carried out for states with arbitrary quantum numbers (the principal and orbital quantum numbers n and , respectively) using forth-order perturbation theory in the shifted expansion parameter 1∕k, where k = N + 2 − a. Here, N is the number of spatial dimensions and (a) is a suitable shift parameter that will be discussed later.…”