Quantum field theories are central to both Condensed Matter and High-Energy Physics. In this article, we show how a typical field theoretical formalism can be pedagogically constructed by generalizing the solution of a harmonic oscillator to a large number of degrees of freedom. In the continuum limit, this method leads to the quantization of the field of a vibrating stretched string as well as to the existence of phonons as elementary excitations ("particles") of this field. The procedure can be used as an elementary introduction to quantum field theory by means of tools taught at an undergraduate course in Quantum Mechanics.
