A particle of mass \(m\) can move along the positive \(x\) axis only, subject to a Hooke's-law spring force \(F=-k x\). That is, there is an impenetrable wall at \(x=0\) preventing it from reaching negative \(x\), and for positive \(x\) there is a spring force attracting the particle back towards the origin. Find the allowed energies of the particle according to the "old quantum theory." Compare these energy levels with those for a particle moving anywhere on the \(x\) axis subject to a spring force \(F=-k x\) attracting it to \(x=0\).