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小山工業高等専門学校研究紀要

Bound states with Vector and Scalar Square Well Potentials

洋一 柴田

Published Mar 1, 1995• 0 citations
OpenAlex

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The Klein–Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V v + V s =constant. These intrinsically relativistic and isospectral problems are solved in the case of squared hyperbolic potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail and the effective Compton wavelength is revealed to be an important physical quantity. It is revealed that a boson is better localized than a fermion when they have the same mass and are subjected to the same potentials.
The Klein–Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V v = V s +constant. These isospectral problems are solved in the case of squared trigonometric potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfunctions are discussed in some detail. It is revealed that a spin-0 particle is better localized than a spin-1/2 particle when they have the same mass and are subjected to the same potentials.