Classical Mechanics vs Quantum Mechanics

[Ishida52134]

Why is it that in the damped simple harmonic equation, the force constant can take on all values, but the force constant corresponding to the classical harmonic oscillator potential in the Schrödinger equation can only take on discrete eigenvalues?

 

[The_Duck]

the force constant corresponding to the classical harmonic oscillator potential in the Schrödinger equation can only take on discrete eigenvalues

The force constant can be anything you want. The *energy* eigenvalues of the harmonic oscillator Hamiltonian are discrete.