Simple expressions for energies

some general properties of the spectrum of the confined hydrogen atom are considered, leading to a simple expression for the energies. It may be noted that since the confining model potentials are qualitative simulations of complicated situations, a qualitative description of the spectrum is very useful. 

For R - oo, the hydrogenic system with the confining potential in Equation (2.2) tends to the free hydrogenic system, and the energies tend to 

We now combine the expressions in Equations (3.35) and (3.38), and consider a simple interpolation 

For the determination of the parameter b in the expression for E in Equation (3.39), we note that the asymptotic behaviour of the hydrogenic wave function for large r is 

Comparing this with the corrections to the hydrogenic energies in Equation (3.39) for large R, 

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A simple expression for energy transfer by exchange interaction can be found assuming hydrogen-like electronic wave functions > 0)... 

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