The Hamiltonian \((p^ 2+m^ 2)^{1/2}-\alpha/r\) near the critical value \(\alpha_ c=2/\pi\). (English) Zbl 0883.47084

Spectral properties of the relativistic Hamiltonian \((p^2+m^2)^{1/2}-{\alpha \over r}\) near the critical value of the coupling constant \(\alpha_c={2 \over \pi}\) are investigated. The methods are based on the introducing of special holomorphic family of operators and usage of the Mellin transformation.


47N50 Applications of operator theory in the physical sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
Full Text: DOI


[1] DOI: 10.1103/PhysRevD.50.5443
[2] DOI: 10.1103/PhysRevD.50.5443
[3] DOI: 10.1103/PhysRevD.50.5443
[4] DOI: 10.1007/BF01609852 · Zbl 0375.35047
[5] DOI: 10.1016/0370-2693(94)90831-1
[6] DOI: 10.1103/PhysRevA.31.2020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.