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.
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