The schematic representation of the shell-confined model defined by the inner radius and the outer radius . The spherical boundaries correspond to the impenetrable walls located at the radial nodes of the chosen free hydrogen atom states.
The plot of free hydrogen radial wave function vs . The four radial nodes are shown as , , , and . The points and correspond to and , respectively. With chosen at , , , , the state. , , , yield state. and , , denote and states, respectively. These shell-confined states have energy equal to that of free hydrogen state which define the incidental degeneracy.
Shell-confined hydrogen atom calculations of energy , Kirkwood polarizability , and Buckingham polarizability , corresponding to ns states. The inner and outer radii of impenetrable spherical confinement are given by and . A11 values are in a.u.
A comparison of Kirkwood polarizability and Buckingham polarizability with the Stemheimer perturbation-numerical estimate corresponding to the shell-confined states of hydrogen atom. The inner and outer radii of impenetrable spherical confinement are given by and that are situated on the locations of the consecutive nodes of the various ns states of the free hydrogen atom . All values are in a.u.
Simultaneous degeneracy for the shell-confined hydrogen atom states defined by and with with one of the confining boundaries at
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