1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Zero-Point Energy

  1. Oct 24, 2005 #1
    "Consider a particle with mass m moving in a potential U=1/2kx^2, as in a mass-spring system. The total energy of the particle is E=p^2/(2m)+1/2kx^2. Assume that p and x are approximately related by the Heisenburg Uncertainty Principal, px approximately equals h.
    a) Calculate the minimum possible value of the energy E, and the value of x that gives this this minimum E. This lowest possible energy, which is not zero, is called the zero-point energy.
    b) For the x calculated in part (a), what is the ratio of kinetic to potential energy of the particle?" -University Physics, by Young and Freedman pg. 1517

    I do not know how to answer this question.
    For (a), I assume that you need to take the derivative of E=p^2/(2m)+1/2kx^2 to minimize it, but in respect to what variable?
    For (b), since E=U+KE, the ratio must be (E-1/2kx^2)/(1/2kx^2), but I am unsure of what that would be without part (a).

    Thanks for your help!
     
  2. jcsd
  3. Oct 24, 2005 #2

    Physics Monkey

    User Avatar
    Science Advisor
    Homework Helper

    The problem tells you to assume that p and x are approximately related in a certain specific way by the Heisenberg Uncertainty Principle. Try solving this relation for p in terms in x and plugging into the Hamiltonian. Can you find a minimum of the resulting expression?

    This is a standard way to estimate the ground state energy of a bound system.
     
  4. Oct 24, 2005 #3
    What is the "Hamiltonian" that you refer to?
    Thanks for your help.
     
  5. Oct 24, 2005 #4

    Physics Monkey

    User Avatar
    Science Advisor
    Homework Helper

    Sorry, the Hamiltonian is just the energy.
     
    Last edited: Oct 24, 2005
  6. Oct 24, 2005 #5
    What energy (E, KE, or U)?
     
  7. Oct 25, 2005 #6

    Physics Monkey

    User Avatar
    Science Advisor
    Homework Helper

    Come on now, AQF, work with me here. I can't just tell you answer. What energy are you trying to minimize?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Zero-Point Energy
Loading...