38 citations · 55 across the 6 of their papers we have counts for
6 papers
The Anisotropic Gaussian Semi-Classical Schrödinger Propagator
Panos D. Karageorge, George N. Makrakis
We present a construction of the Anisotropic Gaussian Semi-Classical Schrödinger Propagator, emblematic of a class of Fourier Integral Operators of quadratic phase kernels related…
Asymptotic Approximations for the Phase Space Schrodinger Equation
Panos D. Karageorge, George N. Makrakis
We consider semi-classical time evolution for the phase space Schrödinger equation and present two methods of constructing short time asymptotic solutions. The first method consist…
Asymptotics for the Phase Space Schrödinger Equation
P. D. Karageorge, G. N. Makrakis
We consider semi-classical time evolution for the phase space Schrödinger equation. We construct a semi-classical phase space propagator in terms of semi-classical wave packets by…
Asymptotic Solutions of the Phase Space Schrodinger Equation: Anisotropic Gaussian Approximation
P. D. Karageorge, G. N. Makrakis
We consider the singular semiclassical initial value problem for the phase space Schrodinger equation. We approximate semiclassical quantum evolution in phase space by analyzing i…
Counting nodal domains on surfaces of revolution
Panos D. Karageorge, Uzy Smilansky
We consider eigenfunctions of the Laplace-Beltrami operator on special surfaces of revolution. For this separable system, the nodal domains of the (real) eigenfunctions form a chec…
Can one count the shape of a drum?
Sven Gnutzmann, Panos D. Karageorge, Uzy Smilansky
Sequences of nodal counts store information on the geometry (metric) of the domain where the wave equation is considered. To demonstrate this statement, we consider the eigenfuncti…