Scientists such as Einstein, Boltzmann, Leibniz, and Kepler understood that musical and scientific thought are deeply linked. Composers have incorporated science into music in literal and metaphorical ways, especially within the last century. In this same span of time, new models in science and music have proliferated. Aside from a few projects, little has been done to meaningfully link quantum physics and music. This dissertation documents my efforts to represent science and, in particular, quantum physics in music through theory, software development, and interpretation. A broad discussion of scientific metaphor in music using two of my compositions as case studies is followed by a look at classical physics in composition and in designing the musical software CHON. In the following chapters, quantum physics and music are brought together through an introduction and examination of my new software application, QHOSYN, and my newest piece, Psi.