Transcription of Georgia Tech PHYS 6124 Mathematical Methods …
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Georgia Tech PHYS 6124 Mathematical Methods …
Georgia tech phys 6124 Mathematical Methods of physics IInstructor: Predrag Cvitanovi cFall semester 2012 Homework Set #6due October 9, 2012== show all your work for maximum credit,== put labels, title, legends on any graphs== acknowledge study group member, if collective effort[All problems in this set are from Goldbart]Problem 1) Linear differential operatorsa) Consider the differential operatorL= ) Find a weight functionwso that the operator is self-adjoint, and findthe corresponding surface ) Consider separately the following boundary conditions for the func-tions on whichLacts:[ ]u(0) =u(2 ) =0,[ ]u(0) =u(2 ),[ ]u(0) =u (2 ) = each case, construct the adjoint boundary conditions and hence de-termine whether the given boundary conditions confer hermiticity which set(s) of boundary conditions would you anticipate thatLpos-sesses a complete set of orthogonal eigenfunctions?
Georgia Tech PHYS 6124 Mathematical Methods of Physics I Instructor: Predrag Cvitanovic´ Fall semester 2012 Homework Set #6 due October 9, 2012 == show all your work for maximum credit,
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