Question

How the zero point energy for a simple harmonic oscillator is consistent with the heisenberg uncertainty principle?

Answer 1

✔The zero-point energy is the lowest energy that a particle has when it is confined within a finite volume. By the uncertainty principle, the zero-point energy cannot be zero. ... As a result, the uncertaintyin its momentum is zero. By Heisenberg's uncertainty principle, theuncertainty in its position should be infinite

Answer 2

Substituting gives the minimum value ofenergy allowed. This is a very significant physical result because it tells us that theenergy of a system described by a harmonic oscillator potential cannot have zero energy.The energy of the ground vibrational state is often referred to as "zero point vibration".