Some asymptotic (n → infinity) properties of hydrogen-like states bar n 1 m > and on the use of the correspondence principle

Some results obtained with the quantal wavefunctions are compared, as n → infinity, with those obtained from the Bohr-Sommerfeld picture. In particular, it is shown that the probability to find the electron in the classically forbidden domain may not be negligible even when all the quantum numbers go to infinity, a fact which leads one to analyse the conditions for using the correspondence principle. (author)