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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.

MSC:

35P15 Estimates of eigenvalues in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis

Citations:

Zbl 0708.00010
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