A surprising synergy between classical and quantum mechanics to help students understand both.

In 1930, Born and Jordan wrote Elementare Quantummechanik. When describing how to solve the harmonic oscillator, they showed an interesting approach for how to decouple the classical Hamiltonian equations of motion. This approach can be generalized to the Kepler problem and many other potentials. If one introduces quantization and elevates position and momentum to operators, the same approach also solves the quantum problems via the factorization method. Using these methods in tandem will help students make abstract quantum ideas more concrete by relating them to classical counterparts. It may even be possible to formulate a new classical-quantum correspondence from the ground-state by using these ideas.