17 Suppose a half-integer /-value, say , were allowed for orbital angularmomentum. FromL,Y,212(0,$)= 0,we may deduce, as usual,Y12.12(0,4) a e'0/2Vsin@.Scanned by CamScanne.Problems245Now try to construct Y/2,-1/2(0, $); by (a) applying L. toY1/2,1/2(8,); and (b) using L Y/2, -1/2(0, $) =0. Show that the twoprocedures lead to contradictory results. (This gives an argument againsthalf-integer /-values for orbital angular momentum.)

The Orbital Angular Momentum is a property of an electron's rotary movement that is related to the…

17, Búppose a half-integer l-value, say , were allowed for orbital angular momentum. From L, Y;/2.1/2(0,4) = 0, we may deduce, as usual, Y1/2.12(0,4) a e'0/2Vsin@ . Scanned by CamScanr Problems 245 Now try to construct Y/2,-1/2(6, ); by (a) applying L. to Y/2.1/2(8,); and (b) using L Y,/2, - 1/2(0, $)-0. Show that the two procedures lead to contradictory results. (This gives an argument against half-integer /-values for orbital angular momentum.)

17, Búppose a half-integer l-value, say , were allowed for orbital angular momentum. From L, Y;/2.1/2(0,4) = 0, we may deduce, as usual, Y1/2.12(0,4) a e'0/2Vsin@ . Scanned by CamScanr Problems 245 Now try to construct Y/2,-1/2(6, ); by (a) applying L. to Y/2.1/2(8,); and (b) using L Y,/2, - 1/2(0, $)-0. Show that the two procedures lead to contradictory results. (This gives an argument against half-integer /-values for orbital angular momentum.)