4.7 (a) Let (x,1) be the wave function of a spinless particle corresponding to a plane wave in three dimensions. Show that (x,-1) is the wave function for the plane wave with the momentum direction reversed. (b) Let x (1) be the two-component eigenspinor of o- with eigenvalue +1. Using the explicit form of x() (in terms of the polar and azimuthal angles and y that characterizea), verify that -iazx"() is the two-component eigenspinor with the spin direction reversed. Use the following information to solve the question (a) is proved in (4.4.59) and (4.4.60) of text. (b) The wave function of a plane, wave ¹P.X/X can be complex without violating tice reversal invariance, because it is degenerate with e-ip.X/X HO|n) = OH|n) = En\n), (4.4.59) (x'In) = (x'\n)* (4.4.60)

4.7 (a) Let (x,1) be the wave function of a spinless particle corresponding to a plane wave in three dimensions. Show that (x,-1) is the wave function for the plane wave with the momentum direction reversed. (b) Let x (1) be the two-component eigenspinor of o- with eigenvalue +1. Using the explicit form of x() (in terms of the polar and azimuthal angles and y that characterizea), verify that -iazx"() is the two-component eigenspinor with the spin direction reversed. Use the following information to solve the question (a) is proved in (4.4.59) and (4.4.60) of text. (b) The wave function of a plane, wave ¹P.X/X can be complex without violating tice reversal invariance, because it is degenerate with e-ip.X/X HO|n) = OH|n) = En\n), (4.4.59) (x'In) = (x'\n)* (4.4.60)