Abstract
Various aspects of critically bound quantal ground states close to the threshold in one, two, and three dimensions are examined in nonrelativistic quantum mechanics using attractive square-well and delta-function potentials. The mathematical and physical reasons are presented for the nonoccurrence of the bound state in the case of three dimensions and its occurrence in one and two dimensions for infinitesimally small strengths and ranges of the potential. Also analyzed is the condition for critical binding in relativistic quantum mechanics using the Klein–Gordon equation in one, two, and three dimensions. Corresponding features for the case of the Dirac equation in one and three dimensions are briefly discussed.
Published Version
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