[UPSC IFoS 2024] Schrodinger’s Wave equation and applications (Q120, 15M)

Consider a particle of mass m moving freely between x = 0 and x = a inside an infinite square well potential. Calculate the expectation values \langle x \rangle_n, \langle p \rangle_n, \langle x^2 \rangle_n and \langle p^2 \rangle_n, and compare them with their classical counterparts.