Consider a harmonic oscillator with constant k, given by V(x) = kx². a) Apply the variational method to determine a maximum bound to the energy of the ground state and the first excited state of this oscillator. For the base state, use the function: f(a.a1.... 1.;)(x) = (ao + a₁x + a₂x² + +ai-1x²-¹)e-ai x², a manon leaving as only nonzero parameters a_0 and a_i, noticing that asking for f to be normalized makes them not independent. For the first excited state considers the same f with a_1 and a_i as only parameters, which once again, they won't be independent. Compare your results with the exact solutions you you know. b) Now suppose we slightly modify the spring constant, k→ (1+ɛ)k, and uses perturbation theory to calculate the correction to the first order of the allowed energies. Start by identifying who plays the role of H', and conclude by comparing your result with the exact solution you know for this potential. Expressions you may use: (H+ AH')|) = Elv), PLEASE WRITE THE STEP BY STEP WITH ALL THE ALGEBRA AND ANSWER ALL THE PARAGRAPHS. PLEASE HELP ME