At one instant a particle is described by the real
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · The formalism of quantum mechanics
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The Schrödinger equation and the Born rule
Problem
At one instant a particle is described by the real, triangular wave function Ψ(x)={A(a−∣x∣)0∣x∣<a∣x∣>a for some length a>0, with A real and positive.
((a)) Find A.
((b)) State ⟨x⟩ and ⟨p⟩, giving your reasoning rather than computing an integral.
((c)) Find ⟨x2⟩ and hence Δx.
((d)) Find Δp, and the product ΔxΔp as a multiple of ℏ.