2. When an atom is placed in an electric field, a dipole moment u = a is induced, where is the field strength and a is the polarizability of the atom. The energy change due to the interaction of this induced dipole with the field is AE = -ae/2. Consider an H atom in an electric field oriented in the z-direction. The field introduces a perturbation H) = eer coso, where r, 0, and o are the electron's coordinates. e re A. Use the trial wave function y, =c41s +c, Y 2 pe to variationally compute the ground state energy of the system, where the normalized Is and 2p, eigenfunctions are: 1 1 e2 V 1s = 4:00(r,0,0)= ; 42 m2 = Y 210(r,0,0) = 24. cose, and En , V 32na 82 Assume that e is "small" and expand your answer to order to determine the polarization, a. Recall H2 that for the 2x2 Secular Determinant, when IH 21