B2 a) Consider a particle of mass M described by the non-relativistic Hamiltonian À, = +Û. Show that the lowest order re

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B2 A Consider A Particle Of Mass M Described By The Non Relativistic Hamiltonian A U Show That The Lowest Order Re 1 (48.33 KiB) Viewed 43 times

B2 a) Consider a particle of mass M described by the non-relativistic Hamiltonian À, = +Û. Show that the lowest order relativistic correction to the 2M Hamiltonian is Ĥ where c is the speed of light. 8MP [6 marks] b) Show that the first order energy shift of a non-degenerate state with unperturbed energy E, due to , be expressed can as SEP 200 ((E5)-28(616)+(6.1736). 2Mc? [6 marks] c) Calculate the first order energy shift 8E"due to Ĥ, for the energy levels of a one-dimensional harmonic oscillator of mass M and angular frequency o with potential energy operator i = 5M08. Me 31° (21? + 2n+1) Show that 8E 32 Mc [11 marks] d) Show that the first order energy shift due to h, for the ground state energy of where E e? is the 88, a. an electron in a hydrogen atom is SE 5(E) 2m.c? ground state energy and a, is the Bohr radius. The radial part of the ground state wavefunction is R. (O)= a [7 marks]