section_path: Examples/Harmonic oscillator
section_name: Harmonic oscillator
paragraph_text: Harmonic oscillator
  
  As in the classical case, the potential for the quantum harmonic oscillator is given by
  
  This problem can either be treated by directly solving the Schrödinger equation, which is not trivial, or by using the more elegant "ladder method" first proposed by Paul Dirac. The eigenstates are given by
  
  where H are the Hermite polynomials
  
  and the corresponding energy levels are
  
  This is another example illustrating the discretization of energy for bound states.