The Supersymmetric Quantum Mechanics example presented in this work proposes a modern approach to understanding complex quantum systems using path integral methods. The harmonic oscillator is a paradigmatic system widely studied in introductory Quantum Mechanics courses, and the application of supersymmetry in this context provides an efficient tool for exploring nontrivial relationships between different quantum states. The combination of supersymmetry with the path integral formalism offers a clear perspective on quantum fluctuations and state transitions, providing valuable insights into the intrinsic nature of physical systems in their quantum description.

keywords
Supersymmetric Quantum Mechanics; Harmonic oscillator; Path integral formalism.