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Minimum uncertainty for antisymmetric wave functions

L. L. Salcedo

Abstract

We study how the entropic uncertainty relation for position and momentum conjugate variables is minimized in the subspace of one-dimensional antisymmetric wave functions. Based partially on numerical evidence and partially on analytical results, a conjecture is presented for the sharp bound and for the minimizers. Conjectures are also presented for the corresponding sharp Hausdorff-Young inequality.

Minimum uncertainty for antisymmetric wave functions

Abstract

We study how the entropic uncertainty relation for position and momentum conjugate variables is minimized in the subspace of one-dimensional antisymmetric wave functions. Based partially on numerical evidence and partially on analytical results, a conjecture is presented for the sharp bound and for the minimizers. Conjectures are also presented for the corresponding sharp Hausdorff-Young inequality.

Paper Structure

This paper contains 1 section, 35 equations, 1 figure.

Table of Contents

  1. Proof of Lemma 1.

Figures (1)

  • Figure 1: Best minimizer of ${\cal S}$ obtained through a 128-dimensional approximation to ${\cal H}_-$ (cf. eq. (\ref{['eq:4']})). The function is purely real and also satisfies $\widetilde{\psi}=+i\psi$. The corresponding value of ${\cal S}$ is $0.61370581$ .