Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 4.5, Problem 4.45P

(a)

To determine

The expression for Hamiltonian as given in equation 4.199 from equation 4.190.

(b)

To determine

The expression as given in equation 4.211 from equation 4.210.

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Problem 2.27: Determine the velocity for which the discrepancy between the classical expression for the kinetic energy and the true expression from relativity differ by 0.01%; in other words, determine the maximum velocity for which we can use the classical expression for the kinetic energy and trust our results to within 0.01% accuracy.
3.9. A particle is traveling at 3c in the x direction. Determine its proper velocity, n (all four components).
Consider a car moving at highway speed u. Is its actual kinetic energy larger or smaller than 1/2 mu2? Make an order-of-magnitude estimate of the amount by which its actual kinetic energy differs from 1/2 mu2. In your solution, state the quantities you take as data and the values you measure or estimate for them. You may find Appendix B.5 useful.
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