Quantum Harmonic Oscillator

The quantum harmonic oscillator is a fundamental model in quantum mechanics representing a particle bound in a potential well, akin to a mass on a spring. It shows how particles behave at the quantum level, where energy levels are quantized—meaning they can only exist in specific amounts. This concept aids in understanding various physical systems, like atoms, where electrons can be thought of as oscillating around a nucleus. It bridges wave mechanics, which describes how particles behave like waves, with matrix mechanics, which uses mathematical matrices to describe quantum states, deepening our understanding of quantum phenomena.