phy246s11_hw5_sol

phy246s11_hw5_sol - I Physics 246 Fifth Homework by...

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I Physics 246 Fifth Homework Set Due: February 25, 20II 1. Extend problem 3 of HW4 by considering the Hamiltonian ,T Js_ ;(p'+q2+^lq') f, I Kz_ [email protected]+qP)' Determine I{r such that the set of comrnutators "I(1, Kz, Je is closed. b) What is Q in this case? c) Repeat the analysis of problem'3 of 'HW4 to determine the allowed spectrum of Js (and thus f/). d) As ) is decreased from zercat what point does the systembreak down? (Physically, the system collapses because the attractive ) term is too strong.) Analyze also the case of ) increasing from zero, What ha,ppens for ) sufficiently large? Z. Consider a particle of mass min the one dirnensional potential V(*) : -V + V'26(x) l"l S o _ 0 l*l>o where V,,Vz > 0. a) Consider a possible ground state of vanishingly small (or zero) energy. Give the wave function for all r in terms of a srnall number of coefficients. State the relevant boundary conditions. b) Sketch the form of the wave function c) Find V as a function of V1.
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