9. Zero-point energy of a harmonic oscillator

📘 Lesson 9 of 21

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What is zero-point energy, and how does it emerge in quantum mechanics?

In this lesson, we revisit the harmonic oscillator and compare classical and quantum treatments of energy. By calculating expectation values for position, momentum, kinetic and potential energy, we reveal a fundamental quantum phenomenon: zero-point energy. Even at its lowest energy state, a quantum oscillator retains unavoidable vibrational motion—unlike in classical physics. This lesson deepens your understanding of quantum expectation values and highlights a key difference between classical and quantum systems.

📝 Solved exercises for this course are available here: https://www.quantphys.com/lessons/qm1