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

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 that gives only two `effective' turning points (defined by the roots of $V(x)+m{c}^2=\pm E$) for a given energy $E$ and satisfies $\min V(x)+m{c}^2\ge 0$. 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.

8 pages, 2 figure

References in corpus (1)

• Ground-state energy eigenvalue calculation of the quantum mechanical well $V(x)=1/2k{x}^2+\lambda x^4$ via analytical transfer matrix method

Cited by in corpus (1)

• Development of the Method of Averaging in Clifford Geometric Algebras