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.
•• Argue that a tunnel junction between two metals has an ohmic resistance; that is, the current I is proportional to the applied voltage V. [Hint: Consider Fig. 14.27(b), and argue that the current is proportional to the number of occupied electronic states on the left that can tunnel into empty states on the right. Note that the number of states per energy interval dN/dE (called the density of states) is very nearly constant for energies within an eV of the Fermi level.]
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