✍ Scribed by Lev Shwartzman
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The two-dimensional Schrodinger operator H a for a spin particle is consid-¨2 ered. The magnetic field b generated by a does not grow in some directions and stabilizes to a positively homogeneous function. It is shown that the spectrum ˜Ž Ž .. Ž Ž .. Ä 4 H a consists of H a and 0 , the latter being
We study the spectral properties of the magnetic Schro dinger operator with a random potential. Using results from microlocal analysis and percolation, we show that away from the Landau levels, the spectrum is almost surely pure point with (at least) exponentially decaying eigenfunctions. Moreover,
A general, energy-separable Faber polynomial representation of the full time-independent Green operator is presented. Non-Hermitian Hamiltonians are included, allowing treatment of negative imaginary absorbing potentials. A connection between the Faber polynomial expansion and our earlier Chebychev