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Generalized Deformed Commutation Relations with Nonzero Minimal Uncertainties in Position and/or Momentum and Applications to Quantum Mechanics
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered.The first one is the most general quadratic commutation relation.The corresponding nonzero minimal uncertainties in position and momentum are determined and the effect on the energy spectrum and eigenfunctions of the harmonic oscillator in an electric field is …