Introduction to Quantum Mechanics · Problem 1.3

The Wave Function — David J. Griffiths

Physics — Quantum Mechanics · gaussian_distribution

Problem

Consider the gaussian distribution ρ(x)=Ae−λ(x−a)2,\rho(x) = Ae^{-\lambda(x-a)^2}, where AA, aa, and λ\lambda are positive real constants. (The necessary integrals are inside the back cover.) (a) Use Equation 1.16 to determine AA. (b) Find ⟨x⟩\langle x \rangle, ⟨x2⟩\langle x^2 \rangle, and σ\sigma. (c) Sketch the graph of ρ(x)\rho(x).

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