Differentiate Fresnel diffraction and Fraunhofer diffraction.

Y(x, t) = y(x)e-it = (Aeikx + Be-ikx) e-iant = Aei(kx-ot) + Be-i(kx+at), (38-25) 13 In Eq. 38-25 keep both terms, putting A = B = yo. The equa- tion then describes the superposition of two matter waves of equal amplitude, traveling in opposite directions. (Recall that this is the condition for a standing wave.) (a) Show that P(x, t)2 is then given by (x, t)² = 2y[1 + cos 2kx]. (b) Plot this function, and demonstrate that it describes the square of the amplitude of a standing matter wave. (c) Show that the nodes of this standing wave are located at where n = 0, 1, 2, 3, ... 1) (1/₁). x = (2n + 1) and is the de Broglie wavelength of the particle. (d) Write a simi- lar expression for the most probable locations of the particle.

Describe how the field radiated by an aperture can be determined from the Huygens Principle using a Fourier Transform

In Compton scattering, for what value of the scattering angle θ the change in the wavelength is maximum.