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Das, Siddhant (2016): Exact energy quantization condition for single Dirac particle in one-dimensional (scalar) potential well. In: Journal of Physics A-Mathematical and theoretical, Vol. 49, No. 21, 215302

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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.

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