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pde waves: string, quantum packet, and e&m 491t = 1u(x,t)23456Figure 18.6 The wave motion of a plucked catenary with friction. (Courtesy of JuanVanegas.)x7. Try the first two normal modes for a uniform string as the initial conditionsfor the catenary. These should be close to, but not exactly, normal modes.8. We derived the normal modes for a uniform string after assuming that k(x)=ω/c(x) is a constant. For a catenary without too much x variation in the tension,we should be able to make the approximationc(x) 2 ≃ T (x)ρ= T 0 cosh(x/d).ρSee if you get a better representation of the first two normal modes if youinclude some x dependence in k.18.5 Unit II. Quantum Wave PacketsProblem: An experiment places an electron with a definite momentum and positionin a 1-D region of space the size of an atom. It is confined to that region by somekind of attractive potential. Your problem is to determine the resultant electronbehavior in time and space.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 491