UWEC CERCA 2026

Liouville’s Theorem states that any bounded, entire function must be constant. Although the results at first may not be obvious, we will explore an intuitive analog for describing the theorem. Furthermore, we will investigate the applications of this theorem and its following corollaries with a focus on thermal physics and chemistry, quantum mechanics, and electrodynamics. These applications include the extrapolation of Laplace’s equation to electrostatic systems, and the posit that no non-constant electric potential can be bound over infinite space. In Thermodynamic instances, it describes phase transitions in the complex plane. Finally, it verifies fundamental ideas of quantum mechanics and quantum field theory, wherein it serves to keep probability distributions bounded.