Quantum Solow Growth Model on Time Scale

Abstract

The quantum Solow growth model is a variation of the Solow growth model that incorporates quantum
effects into the production function. Quantum effects are phenomena that arise from the uncertainty and
randomness of physical measurements. The quantum Solow growth model assumes that the production
function is not deterministic. The production function also incorporates quantum fluctuations, which are
random variations in the output due to quantum interference. The quantum fluctuations can be modelled
by a stochastic process that follows a certain probability distribution In this paper, we generalize Solow
growth model on time scale to quantum calculus of Hudson and Parthasarathy formulation. Existence
and uniqueness of the model is established, using the simple linear combination of the annihilator and
creator operators of the Hudson and Parthasarathy formulation to redefine the labour force and the capital.