A beam of particles is described by the wave function ψ(x)=A exp(ip0x/ℏ) exp(−x^2 /4α^2).
(a) Calculate the expectation value of the momentum ⟨p⟩ by working in the position representation. Hint: First normalize the function by finding the value of A. The integrals in Appendix F of your book may be helpful. (b) Calculate the expectation value of the momentum ⟨p⟩ by working in the momentum representation. Hint: You need to first take the Fourier transform of the wavefunction to get it in the momentum representation.
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