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