Consider a system that consists of two coupled harmonic oscillator with vastly different frequencies. The Hamiltonian H is: 2 \"111312322 H = as + f r... a 2m 2 2m 2 e e meIH 53 .1 +.+wra + 2 "lie 2 me were we: as: aw (a) 1What is the spectrum of the Hamiltonian in the limit 9* = ? Are there any degeneraeies? {h} Find the shift of the ground state energy when gr is turned on to leading non 1.ranishinp; order in g. Make sure to include all the corrections to that order in g, i.e all the contributions with same power of g