Hi, I am trying to find the wavefunction of a coherent state of the harmonic oscillator ( potential mw2x2/2 ) with eigenvalue of the lowering operator: b. I know you can do this is many ways, but I cannot figure out why this particular method does not work. It can be shown (and you can find this easily on the internet) that the eigenvalue b evolves as: b(t)=b0e-iwt What I did was find the coherent state wavefunction u(x,t) by using the eigenfunction equation with the lowering operator a: a[u(x,t)]=b*u(x,t) with a=(mwx+(h-bar)*d/dx)/sqrt(2mw(h-bar)) that gives u(x,t)=const*e-(1/l2)*(x-l*b)2 where l=sqrt(2(h-bar)/mw) now, when I put in the time evolution of b I get: u(x,t)=const*e-(1/l2)*(x-lb0e-iwt)2 (I plugged in b(t) from before in for b) This state does not satisfy the schodinger equation, for one thing it cannot be normalized because the integral over all x of the norm squared of the wavefunction varies in time. This confuses me because b(t) comes from treating the coherent state as a superposition of harmonic oscillator energy eigenstates, which come from the schrodinger equation. Since the schrodinger equation conserves the integral over all x of probability density, why do I get a state which does not do so from harmonic oscilator states (and thus, by extension, the schrodinger equation)? Thanks so much in advance, I have done this over several times over the last day and cannot find out anything I did wrong nor a solution online.