Question

Consider a wave-packet of the form ψ(x) = e −x 2/(2σ 2 ) describing the quantum wave function of an electron. The uncertainty in the position of the electron may be calculated as ∆x = p hx 2i − (hxi) 2 where for a function f(x) the expectation values hi are defined as hf(x)i ≡ R ∞ −∞ dx|ψ(x)| 2f(x) R ∞ −∞ dx|ψ(x)| 2 . Calculate ∆x for the wave packet given above. [Hint: you may look up the Gaussian integral.]

Answer 1