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- W2102008077 abstract "Abstract Relativistic comparison theorems are established for discrete eigenvalues of Klein–Gordon equation with vector and scalar potentials in d -dimensions. Theorem 1 : If V ( λ ) and S ( λ ) depend on a parameter λ , ∂ S / ∂ λ ⩾ 0 , S ⩾ 0 , ∂ V / ∂ λ ⩾ 0 , V ⩽ 0 , E > 0 , then it follows that ∂ E n / ∂ λ ⩾ 0 . Theorem 2 : If S 2 ⩾ S 1 ⩾ 0 , 0 ⩾ V 2 ⩾ V 1 , E > 0 , then the corresponding eigenvalues are ordered as E n ( 2 ) ⩾ E n ( 1 ) . Theorem 3 : If 0 ⩾ V 2 ⩾ V 1 , S 2 ⩾ | S 1 | , E n ( 1 ) > 0 , E n ( 2 ) > 0 , then E n ( 2 ) ⩾ E n ( 1 ) . Some illustrative examples are given." @default.
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- W2102008077 date "2012-01-01" @default.
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- W2102008077 title "Relativistic comparison theorems for the Klein–Gordon equation with scalar and vector potentials in d-dimensions" @default.
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- W2102008077 doi "https://doi.org/10.1016/j.physleta.2011.12.023" @default.
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