Potential well — UPSC CSE 2005 Physics PYQ

Consider a particle of mass m in an infinite one dimensional potential well of width a. The particle is found in the state given by \psi (x) = c \left[ \sin \frac{\pi x}{a} + \frac{1}{2} \sin \frac{2 \pi x}{a} \right] (i) Calculate c. (ii) If a measurement of energy is made, what are the possible results and what are the probabilities for each one of them ?