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Heisenberg's uncertianty principle

  1. Nov 9, 2004 #1
    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. jcsd
  3. Nov 10, 2004 #2

    dextercioby

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    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,[tex] E_{0}=\frac{\hbar\omega}{2} [/tex].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!!
     
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