Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator

2016/05/06 by Pedro Freitas, Freitas, Pedro, James B. Kennedy +1
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1605.01928

Abstract

We derive explicit inequalities for sums of eigenvalues of one-dimensional Schrödinger operators on the whole line. In the case of the perturbed harmonic oscillator, these bounds converge to the corresponding trace formula in the limit as the number of eigenvalues covers the whole spectrum.

Related

• Summation formula inequalities for eigenvalues of Schr "odinger\n operators
• High energy asymptotics and trace formulae for the perturbed harmonic oscillator
• Spectral sum rules for the Schrödinger equation
• Trace identities for commutators, with applications to the distribution of eigenvalues
• Lieb-Thirring type bounds for perturbed Schrödinger operators with single-well potentials