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.

•• The radial equation for l = 0 states in hydrogen was given in (8.79). (a) Verify that this can be rewritten as

(b) For the case that n = 1, prove that is a solution of this equation (that is, calculate the derivative on the left and show that it is equal to the right-hand side).