Rigorous resultats in quantum dynamics

Аннотация

Given a quantum-mechanical Hamiltonian H(p,q) having one degree of freedom, we can construct the Heisenberg equations of motion q = -i[q,H], p = -i[p,H], It is a commonly held belief that such operator differential equations are intractable. However, a technique is presented in this talk that allows one to obtain exact, closed-form solutions for huge classes of Hamiltonians. This technique, which is a generalization of the classical action-angle variable methods, allows one to solve, albeit formally and implicitly, the operator-differential equations of two enharmonic oscillators whose Hamiltonians are H = p2/2 + q4/4 and H = p4/4 + q4/4.