Schrödinger’s equation describes wave-particle duality and although mostly applied to matter at the atomic level, Schrödinger himself did not think it confined to the scale of atoms and fundamental particles.
Indeed, current research at the Massachusetts Institute of Technology extends to how it can even describe human consciousness.
The link between quantum mechanics and the classical world is actually quite clear. The classical world is just the “sum” of probabilities of the atomic world that begin to get very specific and very selective at larger scales.
The elemental components of stock prices are not intuitive and cannot be visualized. But like photons with no rest mass, they nevertheless have energy, momentum, and frequency.
Schrödinger’s time-dependent equation describes how the state of a “particle” varies with time. It incorporates the lowest frequency of oscillation into its formulation. It tells how an operator or nature itself acts on a state which itself is a superposition of basis states.
Mathematically, the equation involves a complex Hermitian acting on an eigenfunction to yield an eigenvalue. The absolute square of the eigenfunction has everything to do with probability.
And it is these probabilities that are the building blocks at the elemental level that contribute to more accurate stock price forecasts.
The total effect of market information appearing at a certain time has a push-pull effect that results
in either a stock price (return) rise or a stock price (return) decline.
In order to describe the evolution of, say, the rate of return r under market information in an idealized world, the stock can be imagined to be similar to a charged particle moving in an electromagnetic field, except the external field of the stock market is market information.
This paper suggests how both the linear and non-linear Schrödinger equations can be used in an optimal investment strategy.