Infinite Potential Box Problem in Fibonacci Calculus

Abstract

We consider the -deformed formalism constructed with some elements of Fibonacci calculus to study the 1D infinite potential box problem where 1-D Schrdinger equation is reframed with well-known modified Fibonacci difference operator and has been solved using q-series solution method. In order to do it, at first, all the selective but essential basics are displayed one by one and -deformed trigonometric functions have been plotted to review and understand the deformed quantum mechanical framework. Hence, on the basis of two parameter deformed algebra, wave functions associated with the particle confined inside the infinite potential box has been obtained. The normalized wave functions and energy expressions have also been obtained for . It is found that all the expressions can be reduced to their conventional form within the limit .