Browsing by Author "Arup Banerjee"

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A new variational wave-function ansatz for confined two-electron atomic systems
(Institute of Physics, 2025) Deepak Singh; Rabeet Singh; Arup Banerjee
In this paper, we propose a simple variational ansatz, Ψ(r⃗1,r⃗2) = C sin (π rc r1) sin( π rc r2) exp(−Z(r1 + r2))[cosh(ar1) + cosh(ar2)][1 + 0.5r12 exp(−br12)], r1 r2 to study confined two-electron atomic systems. Here, r12 = |r-1 −-2| is the inter-electronic distance with the electron coordinatesr-1 andr-2, rc is the radius of the impenetrable well in which the two-electron atoms are confined, and C is the normalization constant. The function sin(πr/rc)/r incorporates the Dirichlet boundary conditions at r = rc needed for the wave function of two-electron systems, and a and b are the variational parameters evaluated by minimizing the total energy functional of confined two-electron atoms. We also calculate the pressure and check the satisfaction of the virial relation for such systems. Our results for the ground-state energy and its components, radial distance moments, and pressure show agreement with the existing literature. © 2025 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.
Calculation of electronic and response properties of a hydrogen atom in soft confinement potential: a variational approach
(Institute of Physics, 2025) Dakshata Mandloi; Rabeet Singh; Arup Banerjee
The electronic properties of atoms confined in finite or infinite boxes with discontinuity have been extensively studied by the researchers. Recently, smooth or continuous versions of such confining potentials given by V conf ( r ) = ( r R ) N with stiffness parameter N and confinement radius R have been considered. This soft-potential coincides with the infinite discontinuous hard-wall potential as N ⟶ ∞ . In this paper, we study the electronic properties of a hydrogen atom confined in a soft-wall potential using a variational approach. For this purpose, we construct the variational wave functions representing the ground state as well as a few low-lying excited states. The variational wave functions yield quite accurate results for a wide range of values of R and N. We also employ the variational ground-state wave function to calculate dipole (α1) and quadrupole (α2) polarizabilities and van der Waals coefficients C6 and C8 © 2025 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.
Modified Le Sech wavefunction for investigating confined two-electron atomic systems
(Springer Science and Business Media Deutschland GmbH, 2024) Rabeet Singh; Arup Banerjee
Abstract: In this article, we propose an alternate approach to study confined two-electron systems using the modified form of the Le Sech wavefunction. In the present approach, rather than using the cut-off factor in the variational wavefunction, we determine it directly by solving Schrödinger like equation. The results for kinetic energies, electron-nucleus interaction, electron–electron interaction, total energies, densities, ionization energies, and moments of confined H- and He atom are compared with the most accurate values found in the literature to show the effectiveness of our method. The present approach applies to a wide range of confinement potentials. We demonstrate it by showing the results for Coulomb, harmonic oscillator, and soft-confinement potentials. Graphic abstract: (Figure presented.). © The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024.