4.7 a. Let y(x.t) be the wave function of a spinless particle corresponding to a plane wave in three dimensions. Show that y* (x.-) is the wave function for the plane wave with the momentum direction reversed. b. Let x(n) be the two-component eigenspinor of a-n with eigenvalue +1. Using the explicit form of x() (in terms of the polar and azimuthal angles ß and y that characterize f) verify that -io₂x*() is the two-component eigenspinor with the spin direction reversed.

4.7 a. Let y(x.t) be the wave function of a spinless particle corresponding to a plane wave in three dimensions. Show that y* (x.-) is the wave function for the plane wave with the momentum direction reversed. b. Let x(n) be the two-component eigenspinor of a-n with eigenvalue +1. Using the explicit form of x() (in terms of the polar and azimuthal angles ß and y that characterize f) verify that -io₂x*() is the two-component eigenspinor with the spin direction reversed.