[UPSC CSE 2006] Foundations of Quantum Mechanics (Q70, 20M)

(i) Calculate the de Broglie wavelength of a thermal neutron at 27~^\circ\text{C} temperature. \hfill 10 (ii) Considering one-dimensional case for free particle, show that the plane wave function is the eigenfunction of a linear momentum operator and kinetic energy operator. \hfill 10