WediscussseparabilityofsolutionstoaSchr?dingerequationthatdescribesacompositequantumsystemandgivesomekindsofHamiltoniansH(t)suchthatthesolutiontoSchr?dingerequationinducedbyH(t)isseparableatanytimeprovidedthatitisseparableatt=0.Forexample,weprovethatiftheHamiltonianHistime-independentandequalstotheproductPA■PBoftwoprojectionsonthesubsystemsKAandKB,respectively,thenthestate|ψ(t)ofthecompositesystemstartingfromaseparableinitial|ψ(0)=|ψA■|ψBisseparableforallt∈[0,T]ifandonlyifeither|ψAisaneigenstateofPA,or|ψBisaneigenstateofPB.
