Abstract
The Sturm-Liouville theory is generalized to Dirac-equation-like systems of ordinary differential equations. It is shown how the comparison theorem and conversion to integral equations can be generalized.
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Yang, C.N.: Monopoles in quantum field theory. Craigie Goddard, Nahm (eds.). Singapore: World Scientific 1982, p. 237
Ma, Z.Q.: Levinson's theorem for Dirac particles moving in a background magnetic monopole field, and Levinson's theorem for Dirac particles with a long-range potential. Phys. Rev. D32, 2203, and 2213 (1985)
For comparison theorems see e.g. Reid, W.T.: Applied mathematical sciences, Vol. 31. Berlin, Heidelberg, New York: Springer 1980
See e.g. Titmarsh, E.C.: Eigenfunction expansions. Part I. Oxford: Oxford University Press
We mean by this thatHφℓ =E ℓφℓ and that φℓ satisfies the boundary conditions atx=0 andx=a
Courant, R., Hilbert, D.: Methods of mathematical physics, Vol. I. New York: Interscience 1953
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Communicated by E. H. Lieb
Dedicated to Walter Thirring on his 60th birthday
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Yang, C.N. Generalization of Sturm-Liouville theory to a system of ordinary differential equations with Dirac type spectrum. Commun.Math. Phys. 112, 205–216 (1987). https://doi.org/10.1007/BF01217686
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DOI: https://doi.org/10.1007/BF01217686