1. For each of the following systems below, identify the zero order Hamiltonian (H) and first order perturbation (H), and write out the general expression for solving for the first-order correction to the energy of state n, E,(). a. A harmonic oscillator with the potential U(x) = d 3 kx + x + x 20 b. A particle constrained to a 1D box 0 x a with the potential U(x) = 0 for 0 x a/2 and U(x) = b * e for a/2 x a 4TE c. A hydrogen atom placed in an external electric field, e. The Hamiltonian operator of this system is H = + er E. 2 (Note: er is the instantaneous dipole moment of an electron. Hint: The dot product of two vectors is: A. B = |A|B|cose)