A New Way of Visualizing Quantum Fields

Abstract

Quantum Field Theory (QFT) is the basis of some of the most fundamental theories in modern physics, but it is not an easy subject to learn. In the present article we intend to pave the way from quantum mechanics to QFT for students at early graduate or advanced undergraduate level. More specifically, we propose a new way of visualizing the wave function $\Psi$ of a linear chain of interacting quantum harmonic oscillators, which can be seen as a model for a simple one-dimensional bosonic quantum field. The main idea is to draw randomly chosen classical states of the chain superimposed upon each other and use a \BW{gray}\color{color} scale to represent the value of $\Psi$ at the corresponding coordinates of the quantized system. Our goal is to establish a better intuitive understanding of the mathematical objects underlying quantum field theories and solid state physics.