Quantum Mechanics: Concepts and Applications · Problem 4.2

One-Dimensional Problems — Nouredine Zettili

Physics — Quantum Mechanics · infinite-square-well-expectation-values

Problem

Consider a particle of mass mm moving freely between x=0x = 0 and x=ax = a inside an infinite square well potential. (a) Calculate the expectation values ⟨X^⟩n\langle \hat{X} \rangle_n, ⟨P^⟩n\langle \hat{P} \rangle_n, ⟨X^2⟩n\langle \hat{X}^2 \rangle_n, and ⟨P^2⟩n\langle \hat{P}^2 \rangle_n, and compare them with their classical counterparts. (b) Calculate the uncertainties product ΔxnΔpn\Delta x_n \Delta p_n. (c) Use the result of (b) to estimate the zero-point energy.

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