Not many systems in physics are exactly solvable. Most of them are too complicated and we have to resort to approximations. One of the few systems that is exactly solvable is the *harmonic oscillator*. In practice, when we think about a harmonic oscillator, we can think about a pendulum: there is always a force acting against any disturbance from the rest position. ![[pendulum.excalidraw.light.svg]] In the case of a harmonic oscillator that force is proportional to the size of the disturbance: if you move the pendulum twice as far out, the force will be twice as large. As a result, a harmonic oscillator is a system that swings back and forth with a constant [[Frequency|frequency]]. ![[harmonic_oscillator_quantum.excalidraw.light.svg]] Also in quantum mechanics, there is an analogue to the harmonic oscillator: also the quantum mechanical harmonic oscillator is exactly solvable. One of its most important features is the equal, [[Discreteness|discrete]] spacing of all [[Energy|energy levels]]. >[!read]- Further Reading >- [[LC Circuit]] >- [[Platform - Superconducting Circuits]] >[!ref]- References