This system can be solved elegantly using the ladder operator method and exploiting the canonical commutation relation.
The Mehler kernel is the propagator of this system's Hamiltonian. The only systems in which all bound orbits are closed are those described by an inverse square force and this system, according to Bertrand's theorem. Some systems modeled using this are better described by the Morse potential, which accounts for a deviation from this system's behavior. The wavefunctions for these systems are proportional to the product of a Gaussian and a (*) Hermite polynomial. This system can be solved elegantly using the ladder operator method and exploiting the canonical commutation relation. The Q factor describes how underdamped one of these systems is. In the small angle approximation, a pendulum can be modeled as one of these. For 10 points, name these systems that exhibit sinusoidal motion.
The Mehler kernel is the propagator of this system's Hamiltonian.
harmonic oscillator [accept prefixes like "simple," "damped," or "quantum"]