A quantum model for the stock market

TL;DR

This paper introduces a novel quantum mechanical model for the stock market, using wave functions and Schrödinger equations to simulate stock price dynamics and analyze market behavior.

Contribution

It develops a quantum econophysics framework with wave functions and operators, applying quantum mechanics principles to model stock market phenomena.

Findings

Wave functions and Schrödinger equations model stock prices.

Analytical solutions for stock return distributions.

Simulation of market equilibrium using quantum well analogy.

Abstract

Beginning with several basic hypotheses of quantum mechanics, we give a new quantum model in econophysics. In this model, we define wave functions and operators of the stock market to establish the Schr\"odinger equation for the stock price. Based on this theoretical framework, an example of a driven infinite quantum well is considered, in which we use a cosine distribution to simulate the state of stock price in equilibrium. After adding an external field into the Hamiltonian to analytically calculate the wave function, the distribution and the average value of the rate of return are shown.