Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

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.

•• If a particle has wave function ψ(x), the probability of finding the particle between any two points b and c is

For a particle in the ground state of a rigid box, calculate the probability of finding it between x = 0 and x = a/3 (where a is the width of the box). Use the hint in Problem 1.

Problem 1

•• Show that the integral which appears in the normalization condition for a particle in a rigid box has the value

[Hint: Use the identity for sin2θ in terms of cos 2θ given in Appendix B.]