Potential well — UPSC Physics Optional IFoS 2024 Paper II

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.