The moments of negative eigenvalues of the Schrödinger operator (Q1385893)

Assume that \(\Omega\) is an arbitrary domain in \(\mathbb{R}^n\), \(n\geq 1\), \(V(x)\) is a real function defined in \(\Omega\), and \(H=- \Delta- V(x)\) is the Schrödinger operator. It is well-known that the negative spectrum of this operator is real. We consider the problem of evaluating the sum \[ S_\gamma= \sum_{\lambda_j< 0}|\lambda_j|^\gamma, \] where \(\lambda_j\) are the negative eigenvalues of the Schrödinger operator.