Potentials of this type possess energy eigenstates of h-bar times omega times the quantity n plus one-half and can be solved algebraically by using raising and lowering operators.
Bertrand's theorem states that stable orbits can only occur for coulomb potentials and these types of potentials. Potentials of this type possess energy eigenstates of h-bar times omega times the quantity n plus one-half and can be solved algebraically by using raising and lowering operators. These objects can be described with a second-order differential equation which equates Newton's Second Law and a displacement times Hooke's constant. For 10 points, identify these objects that experience a restoring force when displaced from their equilibrium point, examples of which include masses on springs and pendulums.
Bertrand's theorem states that stable orbits can only occur for coulomb potentials and these types of potentials.
{quantum} [or {simple}] {harmonic oscillators} [prompt on partial answers]