hw5 - Physics 318: Problem Set 5 Due Wednesday, Feb 27,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 318: Problem Set 5 Due Wednesday, Feb 27, 2008 1. Suppose that two Lagrangians L and L ′ are related by L ′ ( q, ˙ q, t ) = L ( q, ˙ q, t ) + d dt f ( q, t ) (1) where f is some function and q is shorthand for ( q 1 , . . . , q f ). a. By computing the Euler-Lagrange equations for the Lagrangian L ′ , show that the two Lagrangians give the same equations of motion. b. Consider the case of a particle of charge q and mass m moving in electric and magnetic fields parame- terized by a scalar potential Φ and a vector potential A . The Lagrangian for this system is L ( x , ˙ x , t ) = 1 2 m ˙ x 2 − q Φ( x , t ) + q ˙ x · A ( x , t ) . An electromagnetic gauge transformation is a transformation of the form A → A + ∇ ψ , Φ → Φ − ˙ ψ , where ψ = ψ ( x , t ) is an arbitrary function. Show that under such a transformation the Lagrangian transforms as in Eq. (1), and compute the form of the function f . 2. Consider the Lagrangian L ( q 1 , q 2 , ˙ q 1 , ˙ q 2 ) = 1 2 m ( ˙ q 2 1 + ˙ q 2 2 ) − 1 2 mω 2 ( q 2 1 + q 2 2 ) , which describes two uncoupled harmonic oscillators of mass m and frequency ω . Show that this system is invariant under the symmetry operation q ( t ) → e iα q ( t ) , where q ( t ) ≡ q 1...
View Full Document

This homework help was uploaded on 02/24/2008 for the course PHYS 3318 taught by Professor Flanagan during the Spring '08 term at Cornell University (Engineering School).

Page1 / 2

hw5 - Physics 318: Problem Set 5 Due Wednesday, Feb 27,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online