Exact solutions to operator differential equations
Carl M. Bender · Contemporary mathematics - American Mathematical Society · 1994
In this talk we considerthe Heisenberg equations of motion _ --i[q,_¢],_ _--i[p,_, forthe quantum-mechanlcal Hamlltonlan _'f.(p,q) having one degree of freedom.It is a commonly held beliefthat such operator differential equations are intractable.However, a technique is presented here that allowsone to obtain exact,closed-formsolutions forhuge classesofHamil-tox£ians.This technique,which isa generalization of the classical action-angle variable methods, allowsus to solve,albeit formallyand implicitly, the operatordifferential equations of two anharmonic oscillators whose Hamiltonians are _'_ = p2/2 Jr q4/4 and _'_ = p4/4 -I-q4/4.