11 citations · 11 across the 4 of their papers we have counts for
5 papers
Perturbation determinant and Levinson's formula for Schrödinger operators with generalized point interaction
M. Fazeel Anwar, Muhammad Usman, Muhammad Danish Zia
We consider the one dimensional Schrödinger operator with properly connecting generalized point interaction at the origin. We derive a trace formula for trace of difference of reso…
Surgery transformations and spectral estimates of beam operators
Aftab Ali, Muhammad Usman
We introduce type vertex conditions for beam operators, the fourth derivative operator, on metric graphs and study the effect of certain geometrical alterations (graph surgery)…
Surgery transformations and eigenvalue estimates for quantum graphs with vertex interactions
Aftab Ali, Muhammad Usman
We extend the surgical tool box for quantum graphs to anti-standard and vertex conditions. Monotonicity properties of eigenvalues of graph Laplacian with interactions at…
On some sharp spectral inequalities for Schrödinger operators on semi-axis
Pavel Exner, Ari Laptev, Muhammad Usman
In this paper we obtain sharp Lieb-Thirring inequalities for a Schrödinger operator on semi-axis with a matrix potential and show how they can be used to other related problems. Am…
Trace formulas for Schrödinger operators on the half-line
Semra Demirel, Muhammad Usman
We study the scattering problem for the Schrödinger equation on the half-line with Robin boundary condition at the origin. We derive an expression for the trace of the difference o…