Calculation of electronic and response properties of a hydrogen atom in soft confinement potential: a variational approach

Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>conf</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>r</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mfrac> <mml:mi>r</mml:mi> <mml:mi>R</mml:mi> </mml:mfrac> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> with stiffness parameter N and confinement radius R have been considered. This soft-potential coincides with the infinite discontinuous hard-wall potential as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo stretchy="false">⟶</mml:mo> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:math> . 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 ( α 1 ) and quadrupole ( α 2 ) polarizabilities and van der Waals coefficients C 6 and C 8 .