Minimum uncertainty products via the variational principle

Abstract

The problem of finding the class of wave-packets ψ which minimizes the quantum mechanical uncertainty product Δ x Δ p is handled via the constrained variational principle. This leads to a harmonic-oscillator type wave equation for ψ whose explicit solutions are obtained when the potential V has, or does not have, an infinite step. The method can be fruitfully applied to the quantum cosmology of the inflationary universe.