Hamiltonians

Abstract

The formalism of Hamiltonians and path integrals forms one of the cornerstones of theoretical physics. The branch of knowledge that studies Hamiltonians and path integrals is a vast subject that a single chapter can hardly do justice to [7]. As the study of quantum mechanics shows, there are no theorems or general results that one can focus on; instead, one has important examples that illustrate the general techniques of the subject. A similar approach is taken in this Chapter: important exemplars of finance, which are the Black–Scholes and Merton equations, are analyzed to illustrate how quantum mathematics can be employed to analyze these models. The ‘free particle’ is seen to be the system that the Black–Scholes equation requires, and the simple harmonic oscillator model describes one version of the Merton model.