Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Chapter 14, Problem 14.3P
Show that the equation
is invariant under a Lorentz transformation but not under a Galilean transformation. (This is the wave equation that describes the propagation of light waves in free space.)
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Classical Dynamics of Particles and Systems
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- As you read this page (on paper or monitor screen), a cosmic ray proton passes along the left–right width of the page with relative speed v and a total energy of 14.24 nJ. According to your measurements, that left–right width is 21.0 cm. (a) What is the width according to the proton’s reference frame? How much time did the passage take according to (b) your frame and (c) the proton’s frame?arrow_forwardA linear particle accelerator using beta particles collides electrons with their anti-matter counterparts, positrons. The accelerated electron hits the stationary positron with a velocity of 98 x 106 m/s, causing the two particles to annihilate.If two gamma photons are created as a result, calculate the energy of each of these two photons, giving your answer in MeV (mega electron volts), accurate to 1 decimal place. Take the mass of the electron to be 5.486 x 10-4 u, or 9.109 x 10-31 kg.Note: Assume that the kinetic energy is also converted into the gamma rays, and is included in the two photons.arrow_forwardShow that the one-dimensional p(x) = Ae−ikx and three-dimensional expression p(x, y, z) = Ae−ikr is asolution to the Cartesian form of the Helmholtz equation, ∇2p + k2p = 0arrow_forward
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