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.

•• In Chapter 7 we claimed that an electron confined inside a thin conducting wire was essentially a one- dimensional system. To illustrate this, take as a model of the wire a long thin rigid box of length a and square cross section b × b (with a ≫ b). (a) Using the formula (8.103), write down the ground-state energy for an electron in this box. (b) Write down the energy, measured up from the ground stale, of the general excited state. (c) Do the same for an electron in a one-dimensional box of the same length a. (d) Suppose that a = 1 m and b = 1 mm. Show that the first 1700 (approximately) levels of the electron in the wire are identical to those for the one- dimensional box.