Velocity-Dependent Potentials in the Heisenberg Picture

Abstract
Velocity-dependent potentials are investigated in both the Langrangian and Hamiltonian formalisms. A canonical transformation is introduced so that a consistent formulation is achieved. It is found that the proper Hamiltonian operator should be H=K+116f1(r)[f(r)]2 rather than the customarily used form of K=12p·f(r)p+V(r).