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.
• What are the dimensions of a matter wave Ψ(r, t) describing an electron in three dimensions? What are its SI units? [Hint: Probabilities are dimensionless. (Why?)]
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