## Lower bounds for the spectra of Schrödinger operators with magnetic fields.(English)Zbl 0805.35025

Summary: An explicit representation of lower bounds for the spectra of Schrödinger operators with magnetic fields on $$\sigma$$-compact Riemannian manifolds is given, using the positivity of the Pauli Hamiltonian. This representation is applied to show some asymptotic properties of a stochastic oscillatory integral and the transverse analyticity of the law of a stochastic line integral.

### MSC:

 35J10 Schrödinger operator, Schrödinger equation 35P15 Estimates of eigenvalues in context of PDEs
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