Consider a particle that is conﬁned by a one dimensional quadratic (harmonic) potential of the form...

Consider a particle that is conﬁned by a one dimensional quadratic (harmonic) potential of the form U(x) = Ax2 (where A is a positive real number).

a) What is the Hamiltonian of the particle (expressed as a function of velocity v and x)?

b) What is the average kinetic energy of the particle (expressed as a function of T)?

c) Use the Virial Theorem (Eq. 1.46) to obtain the average potential energy of the particle.

d) What would the average kinetic and potential energies be if U(x) = Ax6?

Eq. 1.46: <V>/<K> = 2/n

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genius_generous answered 1 year ago

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