Unconfined hydrogen atom

We begin by observing that the standard treatment of the normal unconfined hydrogen atom (UHA), solves Schrodinger s equation for a model Hamiltonian with a central-field potential (we use the usual atomic units), specifically... 

Table 2 gives a comparison of the asymptotic values of /is-2p and ai with those of other authors for the hydrogen atom and for specimen values of R > 4. The asymptotic result for a is in error by just 2% at R = 4, and the accuracy increases rapidly as R increases. The first-order correction makes an important contribution to this accuracy in fact, when one examines the deviation of aj0) from the unconfined atom value 9/2, it is found to be in error by approaching 50% for some R > 10, whereas is in error by... 

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