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What do mean by a "solution at r=0"? You have a Schrodinger equation, with a Coulomb potential. You solve it. You get a set of discrete eigenstates and eigenvalues, the lowest of which is the ground state, which is stable. Just in the same way as one would for a harmonic oscillator, or pretty much any other potential. What does the fact that there's a divergence at r=0 have to do with anything?marlon said:Well, yes, ofcourse , but you still don't get the point do you???

The strong decrease in potential energy means what do you think ??? There is no solution for r = 0 because it is not physical so not worthy of mentioning here...