On the dynamics of a particle on a hyperboloid

• We study the classical and quantum free particle on a one-sheeted hyperboloid.
• We solve the solutions of classical equations of motion.
• We identify the Hilbert space and observables for a particle on a hyperboloid.
• We find the stationary solution of the Schrödinger equation.

A free particle moving on a one-sheeted hyperboloid is discussed both at the classical and quantum levels.