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For the harmonic oscillator [V(x)=(1 / 2) k x^2], the allowed energies are En=(n 1 / 2) ħω, (n=0,1,2, …) where ω=√(k / m) is the classical frequency. Now suppose the spring constant increases slightly: k →(1 ϵ) k. (Perhaps we cool the spring, so it becomes less. flexible.) (a) Find the exact new energies (trivial, in this case). Expand your formula as a power series in ϵ, up to second order. (b) Now calculate the first-order perturbation in the energy, using Equation Z.9. What is H^' here? Com
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