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The Relativistic one dimensional Coulomb problem was studied by means of thePath Integral Monte Carlo method. Relativistic and non-relativistic regimes ofthis problem were investigated. The relativistic regime appears at small massesof the particle and (or) at strong coupling. Critical coupling at which thebound state disappears was founded. This law is valid for any finiteregularization of the Coulomb potential and potentially can be testedexperimentally.

The Relativistic one dimensional Coulomb problem and Relativistic PIMC method