Quantum mechanical state equation for describing evolution of projects of financial investment

Abstract

This paper proposes a quantum mechanical state equation for describing evolution of projects of financial investment, while the parameters of this equation well simulate the fundamental elements of financial market, including investment (input), assets loss (assets decrease), assets increase and income (output), the quantum mechanics operators involved in this equation also can reflect the dynamic process and characteristics of the project, so the equation can be taken as the evolution model of a kind of financial investment projects in the market. The entangled state representation is introduced to solve this equation and its solution is obtained in an infinite operator-sum form, which exhibits the link between the initial state and final state, i.e., the dynamic process of the financial investment project. As an example, we derive the evolution law of a pure investment project in financial market, which conforms with the evolution trend of the market. In solving the equation we also find a new state which we name it as the binomial-negative binomial entangled state. Throughout the discussions we make full use of Dirac's symbolic method and the technique of integration within an ordered product (IWOP) of operators.