The 'reason' electrons do not collapse into the nucleus of atom is due to the standing wave nature of the electron. This is all fine and dandy. My question, essentially, is why the same does not hold true for positronium (in which an electron orbits a positron). Shouldn't the electron demonstrate here some form of standing wave character here as well? Considering the Schrodinger equation for both systems, the only difference is the reduced mass, which thus leads to a different energy spectrum. Of course, the real result would make use of the Bethe equation, etc.. But I fail to see why this should lead to the instability of positronium. An explanation would be greatly appreciated. Thank you in advance.