Seminario interdisciplinare
ore
16:00
presso Aula Seminario VIII piano
Plan of the talk.
1. Classical Kepler problem. The difference between 1/r and 1/r^2
potentials: in the second case the particle may fall to the centre.
2. Spin zero particle in quantum mechanics. Schrodinger equation and
Hilbert space of states. Connection between the conservation of mass and
self-adjointness of the quantum Hamiltonian.
3. Eigenfunction decomposition for Schrodinger operator with sufficiently
good potentials. The spectral measure.
4. Quantum Kepler problem. For strong attractors the Schrodinger operator
becomes non-self-adjoint.
5. Special class of singular 1-dimensional Schrodinger operators -
spectrally meromorphic operators. The natural indefinite scalar product
for this problem.