a. Let (x, t) be the wave function of a spinless particle corresponding to a plane wave in three dimensions. Show that *(x, t)

a. Let ψ(x, t) be the wave function of a spinless particle corresponding to a plane wave in three dimensions. Show that ψ*(x, – t) is the wave function for the plane wave with the momentum direction reversed.

b. Let x(n) be the two-component eigen spinor of σ ∙ ñ with eigenvalue + 1. Using the explicit form of x(ñ) (in terms of the polar and azimuthal angles β and γ that characterize n) verify that – iσ₂X*(n) is the two-component eigen spinor with the spin direction reversed.