By J. M. Cassels FRS (auth.)

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P, in the limit X~ oo. Instead it oscillates finitely around the mean value zero as X increases, with the amplitude {7r(p'- p )}- 1 . Steps may reasonably be taken to damp out these oscillations, by modifying the momentum eigenfunctions at extremely large values of jxj. After all, the eigenfunctions actually enter into calculations when scalar products with them of physical wave functions 1/J are taken. It is unlikely that 1/J will be significant as far away as the moon, let alone at infinity. Thus the scalar products will not be affected by the introduction of a factor which differs from unity only at extremely large jxj.

5), and the chance that the momentum will be found to have the value p. 17). The limits of integration are x = ±L/2, and the arbitrary length L must be set very large so that all values of x for which 1/1 is significant are covered. With that condition lc. 12 is proportional to 1/L, which looks puzzling at first sight. )IZ, defined so that the chance of the momentum being found with a value between p. and p. + 8p. )IZ 8p•. , and so the density of states in momentum space, which is proportional to L, becomes a factor.

40) 1 1, Clearly 5(1-1') is a highly singular mathematical function, which only has a meaning when it appears in an integral similar to the one that defines it. 41) 1, The 5-function is only non-zero when its argument is zero, and so a reversal in sign of the argument has no effect. The last two equations are still satisfied when 5(l' -l) is substituted for 5(1-1'). 40), ensures that the total chance of getting a result from a measurement of l is unity. 11). 16). 3) The right-hand side here is clearly the expectation value of the operator in the parentheses, so that, (afat Y d A -(l)= - - -i [ f.