The dynamic nature of quantum physical models make them well-suited to creative sound design and musical purposes through sonification and metaphor. These systems outline a new class of time-varying stochastic physical models. QHOSYN is a software synthesizer for simulating and sonifying the most fundamental of quantum mechanical models: the quantum harmonic oscillator. This basic model is used in physics to describe a plethora of more complex systems, and so it serves as a solid foundation for work in sonifying quantum systems. QHOSYN runs on Linux, Windows, and MacOS and allows composers and music researchers to explore the sonic potential in this physical model. In this paper, the software is introduced through a discussion of its background, an overview of the physical simulation implementation, a look at the visual interface, a description of the internal sound engine and how it can be extended through OSC, and finally a case study of using the software in composition.