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Non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials. (English) Zbl 1227.65105

The authors present a non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials. They first present a self-contained description of the quadratic projection method. Spectral pollution in the standard Galerkin method using this decomposition and the consequences of unbalancing the number of upper/lower components is discussed. Convergence rates of the method are presented and various numerical examples are given to illustrate the theory discussed.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
35Q41 Time-dependent Schrödinger equations and Dirac equations
47F05 General theory of partial differential operators
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

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References:

[1] Hislop, Proceedings of the Symposium on Mathematical Physics and Quantum Field Theory (Berkeley, CA, 1999) pp 265– (2000)
[2] Triebel, Math. Bohem. 124 pp 123– (1999)
[3] Klaus, Helv. Phys. Acta. 53 pp 463– (1980)
[4] Shargorodsky, J. Operator Theory 44 pp 43– (2000)
[5] Thaller, The Dirac Equation (1992) · Zbl 0765.47023 · doi:10.1007/978-3-662-02753-0
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