The harmonic oscillator is a foundational model in physics, valued for its solvability and broad relevance. When the oscillator’s frequency varies in time—as in ion traps with dynamic fields—it can still be treated analytically in certain cases. This overview presents an exactly solvable example illustrating such behavior.

Episode 5 of Quantum on the Back of an Envelope. In this episode of Quantum on the Back of an Envelope , In this episode of Quantum on the Back of an Envelope, we ask whether a quantum mechanical wave function really has to vanish at infinity — an assumption often made in introductory textbooks and courses. To explore this, we examine a specific example (taken from "Principles of Advanced Mathematical Physics" by Robert D. Richtmyer) of a wave function that is perfectly conti

Episode 4 of Quantum on the Back of an Envelope. In this episode of Quantum on the Back of an Envelope , we explore how frequent observations -- more precisely, projective measurements -- can dramatically alter the time evolution of a quantum system, and in some cases even freeze it altogether. This fascinating phenomenon is known as the quantum Zeno effect.