1. The problem statement, all variables and given/known data Consider as an unperturbed system H0 a simple harmonic oscillator with mass m, spring constant k and natural frequency w = sqrt(k/m), and a perturbation H1 = k′x = k′sqrt(hbar/2m)(a+ + a−) Determine the exact ground state energy and wave function of the perturbed system here a+ and a- are the ladder operators: a+/-=1/sqrt( 2hbar*m*ω)(-/+p^2 +(mωx) ) and H0=1/(2m)*(p^2 +(mωx)^2) = hbar*ω*[(a+)*(a-)+1/2] 3. The attempt at a solution I just need a nudge in the right direction for this one. The questoin confuses me because I didnt realize exact solutions could be found for perturbed systems. we want to solve Hψ=Eψ where H= H0 + λH1 (the unperturbed hamiltonian plus the perturbation) I am confused about the factor of λ on H1. griffiths text says " for the moment we'll take lambda to be a small number, later we'll crank it up to one, and H will be the true hamiltonian" so should I take λ=1? either way, when I write out Hψ=Eψ, i get a very nasty diff. eq. which leads me to believe there is a better method.