Determinant of the Schr\"odinger operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 96 (1993) no. 3, pp. 373-384
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{TMF_1993_96_3_a3,
author = {D. A. Kirzhnits},
title = {Determinant of the {Schr\"odinger} operator},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {373--384},
publisher = {mathdoc},
volume = {96},
number = {3},
year = {1993},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1993_96_3_a3/}
}
D. A. Kirzhnits. Determinant of the Schr\"odinger operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 96 (1993) no. 3, pp. 373-384. http://geodesic.mathdoc.fr/item/TMF_1993_96_3_a3/