The resolvent equation of the one-dimensional Schrödinger operator on the whole axis

DOI10.1134/S0037446612060018zbMath1266.34138MaRDI QIDQ1935729

Elshad H. Eyvazov, Araz R. Aliev

Publication date: 19 February 2013

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

resolvent equationelectric potentialquantum mechanicsmagnetic Schrödinger operatormagnetic potential

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Spectrum, resolvent (47A10) General theory of ordinary differential operators (47E05)

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The inverse spectral problem of some singular version of one-dimensional Schrödinger operator with explosive factor in finite interval, Unnamed Item, Boundary-value problems for the evolutionary Schrödinger equation. I, Representation of the solutions of boundary-value problems for the Schrödinger equation in a Hilbert space, The inverse spectral problem of some singular Sturm-Liouville problems with sign-valued weights, The inverse scattering problem of some Schrödinger type equation with turning point

Cites Work

• Sturm-Liouville operators with singular potentials
• The spectrum and the scattering problem for the Schrödinger operator in a magnetic field
• Deficiency indices and spectrum of self-adjoint extensions of some classes of differential operators
• Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation
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