"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.(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Zero-Point Energy

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