A Schrödinger-type Equation in one Complex Space Variable

We consider a Schrödinger-type equation in one complex space variable built upon first and second-order partial derivation non-self-adjoint operators defined in subspaces of a separable Hilbert space of smooth curves taking values in the Segal–Bergmann space of analytic functions in the complex plane. We build solutions of two types for this equation, essentially using a generalisation of the method of indeterminate coefficients; we show the existence of general solutions using a Fourier–Hilbert base of the space of smooth curves that was previously determined. We present two applications of the Schrödinger-type equation studied. In the first one, we consider a wave associated with an object having the mass of an electron, showing that two waves, when considered as having only a free real space variable, are entangled, in the sense that the probability densities in the real variable are almost perfectly correlated. In the second application, after postulating that a usual package of information may have a mass of the order of magnitude of the neutron's mass attributed to it — and so well into the domain of possible quantisation — we explore some consequences of the model.