Abstract
We present an exact quantization condition for the time independent solutions (energy eigenstates) of the one-dimensional Dirac equation with a scalar potential well characterized by only two 'effective' turning points (defined by the roots of V (x) + mc(2) = +/- E) for a given energy E and satisfying mc(2) + min V (x) >= 0. This result generalizes the previously known non-relativistic quantization formula and preserves many physically desirable symmetries, besides attaining the correct non-relativistic limit. Numerical calculations demonstrate the utility of the formula for computing accurate energy eigenvalues.
Dokumententyp: | Zeitschriftenartikel |
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Fakultät: | Physik |
Themengebiete: | 500 Naturwissenschaften und Mathematik > 530 Physik |
ISSN: | 1751-8113 |
Sprache: | Englisch |
Dokumenten ID: | 47766 |
Datum der Veröffentlichung auf Open Access LMU: | 27. Apr. 2018, 08:13 |
Letzte Änderungen: | 04. Nov. 2020, 13:24 |