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.
•• Evaluate the integral (7.65) to give the average result 〈x〉 (the expectation value) found when the position of a particle in the ground state of a rigid box is measured many times. [Hint: Rewrite sin2(πx/a) in terms of cos2(2πx/a) and use integration by parts.]
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