Muhammad Usman

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math-ph2023

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…

math-ph2022

Surgery transformations and spectral estimates of $δ$ beam operators

Aftab Ali, Muhammad Usman

We introduce $δ$ type vertex conditions for beam operators, the fourth derivative operator, on metric graphs and study the effect of certain geometrical alterations (graph surgery)…

math-ph2022

Surgery transformations and eigenvalue estimates for quantum graphs with $δ^{'}$ vertex interactions

Aftab Ali, Muhammad Usman

We extend the surgical tool box for quantum graphs to anti-standard and $δ^{'}$ vertex conditions. Monotonicity properties of eigenvalues of graph Laplacian with $δ^{'}$ interactions at…

Perturbation determinant and Levinson's formula for Schrödinger operators with generalized point interaction

Surgery transformations and spectral estimates of δ beam operators

Surgery transformations and eigenvalue estimates for quantum graphs with δ′ vertex interactions

Surgery transformations and spectral estimates of $δ$ beam operators

Surgery transformations and eigenvalue estimates for quantum graphs with $δ^{'}$ vertex interactions