Consider the following Hamiltonian:p 12+arH2m 2where y and a are both positive.(a) Determine the ground state value (i.e. minimum energy) of (r) at T 0.(b) Determine the frequency for simple harmonic motion for the limit of small temperatures.(c) Derive an equation for (r) to first order in temperature.

Given, H=p22m-12γx2+αx4 The potential vx=-12γx2+αx4 For the equilibrium, dvdxx=x0=0…

Consider the following Hamiltonian: p 1 H ² + az* 2m 2 where y and a are both positive. (a) Determine the ground state value (i.e. minimum energy) of (z) at T = 0. (b) Determine the frequency for simple harmonic motion for the limit of small temperatures. (c) Derive an equation for (r) to first order in temperature.

Consider the following Hamiltonian: p 1 H ² + az* 2m 2 where y and a are both positive. (a) Determine the ground state value (i.e. minimum energy) of (z) at T = 0. (b) Determine the frequency for simple harmonic motion for the limit of small temperatures. (c) Derive an equation for (r) to first order in temperature.