O. Ogurisu

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Articles: 2

On the number of negative eigenvalues of a multi-dimensional Schrodinger operator with point interactions

Osamu Ogurisu

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 16 (2010), no. 4, 383-392

We prove that the number $N$ of negative eigenvalues of a Schr\"odinger operator $L$ with finitely many points of $\delta$-interactions on $\mathbb R^{d}$ (${d}\le3$) is equal to the number of negative eigenvalues of a certain class of matrix $M$ up to a constant. This $M$ is expressed in terms of distances between the interaction points and the intensities. As applications, we obtain sufficient and necessary conditions for $L$ to satisfy $N=m,n,n$ for ${d}=1,2,3$, respectively, and some estimates of the minimum and maximum of $N$ for fixed intensities. Here, we denote by $n$ and $m$ the numbers of interaction points and negative intensities, respectively.

On the number of negative eigenvalues of a Schrodinger operator with $\delta$ interactions

Osamu Ogurisu

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 16 (2010), no. 1, 42-50

We give necessary and sufficient conditions for a one-dimensional Schrodinger operator to have the number of negative eigenvalues equal to the number of negative intensities in the case of $\delta$ interactions.


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