Consider an electron on a ring of radius ro that is confined to move only on...

 

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Consider an electron on a ring of radius ro that is confined to move only on the ring. A weak electric field is applied such that the perturbation Hamiltonian is eVx H' ro a. What unitless quantity must be much less than one in order to justify the use of perturbation theory? b. To first order, find the m = 0 state. c. Compare your answer in part b) with the zeroth order (unperturbed) m = 0 state. Also, draw a graph comparing the modulus squared of the unperturbed and perturbed (first order) wavefunctions when the unitless quantity in part a) is equal to 0.1. Does this make physical sense? d. To second order, find the energy of m = 1 and m 2 states. Consider an electron on a ring of radius ro that is confined to move only on the ring. A weak electric field is applied such that the perturbation Hamiltonian is eVx H' ro a. What unitless quantity must be much less than one in order to justify the use of perturbation theory? b. To first order, find the m = 0 state. c. Compare your answer in part b) with the zeroth order (unperturbed) m = 0 state. Also, draw a graph comparing the modulus squared of the unperturbed and perturbed (first order) wavefunctions when the unitless quantity in part a) is equal to 0.1. Does this make physical sense? d. To second order, find the energy of m = 1 and m 2 states.

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