Interaction picture as any other operator. In particular, let and be the density matrices in the interaction picture and the Schrödinger picture respectively. If there is probability to be in the physical state |"ψ"〉, then Transforming the Schrödinger equation into the interaction picture gives which states that in the interaction picture, a quantum state is evolved by the interaction part of the Hamiltonian as expressed in the interaction picture. If the operator "A" is time-independent (i.e., does not have "explicit time dependence"; see above), then the corresponding time evolution for "A"("t") is given by In the interaction picture the operators evolve in
Non-physical entity opposed aspects.The dualist school supposes the existence of non-physical entities, the most widely discussed one being the mind. But beyond that it runs into stumbling blocks. Pierre Gassendi put one such problem directly to René Descartes in 1641, in response to Descartes's "Meditations": Descartes' response to Gassendi, and to Princess Elizabeth who asked him similar questions in 1643, is generally considered nowadays to be lacking, because it did not address what is known in the philosophy of mind as the interaction problem. This is a problem for non-physical entities as posited by dualism: by what mechanism, exactly, do they interact