A problem listed for a given section requires an understanding of that section and earlier sections, but not of later sections. Within each section, problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
• We have seen that for a nonrelativistic free particle, the particle’s velocity vpart equals the velocity vpack of the corresponding wave packet [as given by (6.56)]. Prove that the same is true for a relativistic free particle. (Remember the “Pythagorean relation” between E and p.)
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