Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 40, Problem 50P
To determine
To prove that the group speed of the wave is same as the speed of the particle.
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For a free relativistic quantum particle moving with speed u, the total energy of the particle is E = hf = hω = √p2c2 + m2c4 and the momentum is p = h/λ = hk = γmu. For the quantum wave representing the particle, the group speed is υg = dω/dk. Prove that the group speed of the wave is the same as the speed of the particle.
A quantum particle of mass m is placed in a one-dimensional box of length L. Assume the box is so small that the particle’s motion is relativistic and K = p2/2m is not valid. (a) Derive an expression for the kinetic energy levels of theparticle. (b) Assume the particle is an electron in a box of length L = 1.00 × 10-12 m. Find its lowest possible kinetic energy. (c) By what percent is the nonrelativistic equation in error?
The relation for total energy (E ) and momentum (p) for a relativistic particleis E 2 = c2 p2 + m2c4, where m is the rest mass and c is the velocity of light.Using the relativistic relations E = ω and p = k, where ω is the angularfrequency and k is the wave number, show that the product of group velocity(vg) and the phase velocity (vp) is equal to c2, that is vpvg = c2
Chapter 40 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Ch. 40.1 - Prob. 40.1QQCh. 40.2 - Prob. 40.2QQCh. 40.2 - Prob. 40.3QQCh. 40.2 - Prob. 40.4QQCh. 40.3 - Prob. 40.5QQCh. 40.5 - Prob. 40.6QQCh. 40.6 - Prob. 40.7QQCh. 40 - Prob. 1OQCh. 40 - Prob. 2OQCh. 40 - Prob. 3OQ
Ch. 40 - Prob. 4OQCh. 40 - Prob. 5OQCh. 40 - Prob. 6OQCh. 40 - Prob. 7OQCh. 40 - Prob. 8OQCh. 40 - Prob. 9OQCh. 40 - Prob. 10OQCh. 40 - Prob. 11OQCh. 40 - Prob. 12OQCh. 40 - Prob. 13OQCh. 40 - Prob. 14OQCh. 40 - Prob. 1CQCh. 40 - Prob. 2CQCh. 40 - Prob. 3CQCh. 40 - Prob. 4CQCh. 40 - Prob. 5CQCh. 40 - Prob. 6CQCh. 40 - Prob. 7CQCh. 40 - Prob. 8CQCh. 40 - Prob. 9CQCh. 40 - Prob. 10CQCh. 40 - Prob. 11CQCh. 40 - Prob. 12CQCh. 40 - Prob. 13CQCh. 40 - Prob. 14CQCh. 40 - Prob. 15CQCh. 40 - Prob. 16CQCh. 40 - Prob. 17CQCh. 40 - The temperature of an electric heating element is...Ch. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6PCh. 40 - Prob. 7PCh. 40 - Prob. 8PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 22PCh. 40 - Prob. 23PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Prob. 30PCh. 40 - Prob. 31PCh. 40 - Prob. 32PCh. 40 - Prob. 33PCh. 40 - Prob. 34PCh. 40 - Prob. 36PCh. 40 - Prob. 37PCh. 40 - Prob. 38PCh. 40 - Prob. 39PCh. 40 - Prob. 40PCh. 40 - Prob. 41PCh. 40 - Prob. 42PCh. 40 - Prob. 43PCh. 40 - Prob. 45PCh. 40 - Prob. 46PCh. 40 - Prob. 47PCh. 40 - Prob. 48PCh. 40 - Prob. 49PCh. 40 - Prob. 50PCh. 40 - Prob. 51PCh. 40 - Prob. 52PCh. 40 - Prob. 53PCh. 40 - Prob. 54PCh. 40 - Prob. 55PCh. 40 - Prob. 56PCh. 40 - Prob. 57PCh. 40 - Prob. 58PCh. 40 - Prob. 59PCh. 40 - Prob. 60APCh. 40 - Prob. 61APCh. 40 - Prob. 62APCh. 40 - Prob. 63APCh. 40 - Prob. 64APCh. 40 - Prob. 65APCh. 40 - Prob. 66APCh. 40 - Prob. 67APCh. 40 - Prob. 68APCh. 40 - Prob. 69APCh. 40 - Prob. 70APCh. 40 - Prob. 71APCh. 40 - Prob. 72CPCh. 40 - Prob. 73CPCh. 40 - Prob. 74CPCh. 40 - Prob. 75CPCh. 40 - Prob. 76CP
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