# prob1 - PHY 614 : Quantum Mechanics Problem Set No. 1 : Due...

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PHY 614 : Quantum Mechanics Problem Set No. 1 : Due : September 3 ,2010 Problems which are marked with a ? will not be graded. You should nevertheless do them for your own beneﬁt, but you do not need to submit them. Solutions to all the problems will be posted on the website after the due date. There are problems on both sides of this sheet 1. (10 points) The lagrangian for two coupled harmonic oscillators is given by L = m 2 ( ˙ x 1 2 + ˙ x 2 2 ) + k 2 ( x 2 1 + x 2 2 ) - λx 1 x 2 (1) (a) Write down the lagrangian equations of motion, and ﬁnd the solution x 1 ( t ) ,x 2 ( t ) with the initial conditions x 1 (0) = x 2 (0) = 0 and ˙ x 1 (0) = 0 , ˙ x 2 (0) = v 0 . (b) Plot the resulting solutions x 1 ( t ) and x 2 ( t ). 2. (20 points) The lagrangian for a charged particle restricted to move on a two dimensional plane with coordinates x and y in the presence of a magnetic ﬁeld in the z direction perpendicular to the plane is given by L 1 = m 2 ( ˙ x 2 + ˙ y 2 ) + eB 2 ( x ˙ y - y

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## This note was uploaded on 08/30/2010 for the course PHYSICS PH 614 taught by Professor Sumitdas during the Fall '10 term at Kentucky.

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prob1 - PHY 614 : Quantum Mechanics Problem Set No. 1 : Due...

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