The discussion highlights the distinction between classical mechanics and quantum mechanics, specifically regarding the force constant in the damped simple harmonic equation versus the classical harmonic oscillator potential in the Schrödinger equation. While the force constant can assume any value in classical mechanics, the energy eigenvalues of the quantum harmonic oscillator Hamiltonian are quantized, resulting in discrete eigenvalues. This fundamental difference underscores the transition from classical to quantum physics and the implications for energy states.
PREREQUISITESPhysics students, educators, and researchers interested in the foundational differences between classical and quantum mechanics, particularly in the context of harmonic oscillators.
Ishida52134 said:the force constant corresponding to the classical harmonic oscillator potential in the Schrödinger equation can only take on discrete eigenvalues