Around Scott correction term(s)

I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.

Non weylian spectral asymptotics with accurate remainder estimate

V. Ivrii (1990-1991)

Séminaire Équations aux dérivées partielles (Polytechnique)

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Estimates for a number of negative eigenvalues of the Schrödinger operator with intensive magnetic field

Victor Ivrii (1987)

Journées équations aux dérivées partielles

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Recent results on Lieb-Thirring inequalities

Ari Laptev, Timo Weidl (2000)

Journées équations aux dérivées partielles

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We give a survey of results on the Lieb-Thirring inequalities for the eigenvalue moments of Schrödinger operators. In particular, we discuss the optimal values of the constants therein for higher dimensions. We elaborate on certain generalisations and some open problems as well.