Klein-Gordon lower bound to the semirelativistic ground-state energy

Richard L. Hall; Wolfgang Lucha

doi:10.1016/j.physleta.2010.03.006

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arXiv · 0906.2001

Klein-Gordon lower bound to the semirelativistic ground-state energy

Richard L. Hall·Wolfgang Lucha

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Abstract

For the class of attractive potentials V(r) <= 0 which vanish at infinity, we prove that the ground-state energy E of the semirelativistic Hamiltonian H = \sqrt{m^2 + p^2} + V(r) is bounded below by the ground-state energy e of the corresponding Klein--Gordon problem (p^2 + m^2)ϕ= (V(r) -e)^2ϕ. Detailed results are presented for the exponential and Woods--Saxon potentials.

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Richard L. Hall, Wolfgang Lucha. 2010-03-02. Klein-Gordon lower bound to the semirelativistic ground-state energy. https://doi.org/10.1016/j.physleta.2010.03.006

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