# Heisenberg's uncertianty principle

1. Nov 9, 2004

### Physicsiscool

Can anyone help me with this question?

A simple harmonic oscillator can be considered to be a small mass "m" on a spring of a force constant "k" when the force is f = -kx and the potential energy is V(x) = 1/2mw(squared)x(squared) where w = square root of (k/m)

Knowing this I need to show that the minimum value for the energy of the ocillator is E (min) = h(bar) * w

2. Nov 10, 2004

### dextercioby

That's correct.

That's wrong,unless you screw up calculations and end up with the wrong formula written above.The right one is,of course,$$E_{0}=\frac{\hbar\omega}{2}$$.It's called the vacuum energy of the oscillator and it's a pure quantum effect.
Quantum mechanics books find this by two methons.Using Schroedinger's equation or using creation+annihilation operators.The latter is more elegant.The former requires lots of calculating.
Good luck!!