Geodesic
Determinant of the Schrödinger operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 96 (1993) no. 3, pp. 373-384 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the example of the nonrelativistic Schrödinger operator, methods are formulated for calculating the determinant of an elliptic operator on the basis of scattering theory. It is shown that such a determinant is identical to the Jost determinant at zero energy. In the centrally symmetric case, it reduces to ordinary Jost functions and ultimately to the values of the zero-energy wave functions at the origin. The relationship between the determinant of the Schrödinger operator and the characteristics of the scattering resonances and the number of bound states in a field of opposite sign is noted. This makes it possible to find the first terms in the gradient expansion of the determinant as a functional of the potential. The problem of the correlation free energy of a classical plasma serves as a physical illustration. 
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     title = {Determinant of the {Schr\"odinger} operator},
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D. A. Kirzhnits. Determinant of the Schrödinger operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 96 (1993) no. 3, pp. 373-384. http://geodesic.mathdoc.fr/item/TMF_1993_96_3_a3/

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