[UPSC CSE 2002] Foundations of Quantum Mechanics (Q74, 10M)

(i) The wave function of a particle is . \psi(x) = A \exp \left( -\frac{x^2}{a^2} + i k_0 x \right) Find the expectation values of position (x) and momentum (p) for the particle. (ii) A 200 eV increase in the energy of an electron changes its De Broglie wavelength by a factor of two. Calculate the initial De Broglie wavelength of the electron.