Sobolev, A. V. On the asymptotics of discrete spectrum for the Schrödinger operator in electric and homogeneous magnetic fields. (English) Zbl 0718.35069 Order, disorder and chaos in quantum systems, Proc. Conf., Dubna/USSR 1989, Oper. Theory, Adv. Appl. 46, 27-31 (1990). Summary: [For the entire collection see Zbl 0708.00010.] We study the asymptotics of bound states below the bottom of essential spectrum for the Schrödinger operator in a homogeneous magnetic and a decreasing electric field. The electric potential is not assumed to be non-positive. The potential integrated along the direction of the magnetic field is supposed to have a power-like behaviour at infinity. The asymptotics of bound states is shown to be of a power-like character, and its main term is evaluated. Cited in 1 Document MSC: 35P15 Estimates of eigenvalues in context of PDEs 35J10 Schrödinger operator, Schrödinger equation 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis Keywords:bound states; essential spectrum Citations:Zbl 0708.00010 PDFBibTeX XMLCite \textit{A. V. Sobolev}, in: Order, disorder and chaos in quantum systems. Proceedings of a conference held at Dubna, USSR on October 17-21, 1989. Basel etc.: Birkhäuser Verlag. 27--31 (1990; Zbl 0718.35069)