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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 scalarpotential well that gives only two `effective' turning points (defined by theroots of $V(x)+mc^2=\pm E$) for a given energy $E$ and satisfies $\minV(x)+mc^2\geq 0$. This result generalizes the previously known non-relativisticquantization formula and preserves many physically desirable symmetries,besides, attaining the correct non-relativistic limit. Numerical calculationsdemonstrate the utility of the formula for computing accurate energyeigenvalues.

Exact energy quantization condition for single Dirac particle in one-dimensional (scalar) potential well