Question

(a) Use the variational method to estimate the ground state energy of a particle of |mass m in a potential Vx)kx, k > 0. (b) Calculate the energy shift in the ground state and in the degenerate 1t excited state of a 2-dimensional harmonic oscillator H(P2P,2/2m m(x +y)due to the perturbation V 2Axy. (20 pts)

Answer 1

Soluton K O et trial oave function 13 Gaussian b Comstant A Nomaligahion Constant Nor mali'sing of A we alue e1 A - Alous H T <v> -b A

m ol 2 2b 24 - 2 K IA Y2-/2 и 2 164 2 far gocund 8tafe ener9 d<Hy we ham V нЕ 3 k 2m

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pertubahon ha Separskd the digenyate tirs Exted thus ue find hat owr State b amound tshere p