Relation with Quantum Mechanics

As we have previously mentioned, the operator structure of quantum mechanics, p→ − iħ∂∕∂x and e→iħ∂∕∂t, is intrinsically inherent in the proposed theory, assuming conservative external forces f = −∂V∕∂x and gc 2 = −∂V∕∂t. From the relations (10.4), we have p = ∂ψ∕∂x and E = ∂ ψ ∕ ∂ t $$\mathcal {E} = {\partial \psi }/{\partial t}$$ and conservation of energy e + E + V = c o n s t a n t $$e + \mathcal {E} + V = constant$$ immediately gives e = −(∂ψ∕∂t + V ), and this is precisely the structure of the standard operator relations of quantum mechanics. That is, the established structure of the conventional operators of quantum mechanics is embodied in the present approach and arises from conservation of energy.