Classical and Quantum Physics in Selected Economic Models

A growing number of economic phenomena are nowadays described with methods known in physics. The most frequently applied physical theories by economists are: (1) the universal gravitation law and (2) the first and second law of thermodynamics. Physical principles can also be applied to the theory of financial markets. Financial markets are composed of individual participants who may be seen to interact as particles in a physical system. This approach proposes a financial market model known as a minority game model in which securities and money are allocated on the basis of price fluctuations, and where selling is best option when the vast majority of investors tend to purchase goods or services, and vice versa. The players who end up being on the minority side win.

The above applications of physical methods in economics are deeply rooted in classical physics. However, this paper aims to introduce the basic concepts of quantum mechanics to the process of economic phenomena modelling. Quantum mechanics is a theory describing the behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties. The key role in quantum mechanics is played by: (1) the Schrödinger equation describing the probability amplitude for the particle to be found in a given position and at a given time, and as (2) the Heisenberg uncertainty principle stating that certain pairs of physical properties cannot be economic applications of the Schrödinger equation as well as the Heisenberg uncertainty principle. We also try to describe the English auction by means the quantum mechanics methods.