| Abstract: |
| We develop a method, based in the theory of positive commutators, for studying the existence of bound states
for the propagator $(U(t,0))$, at a fixed time $t$, associated to
time dependent Schr\odinger equation
$$
i\, \varphi_t = H(t)\varphi .
$$
We apply this method to shoe the non existence of solitons for the Hamiltonian of a quantum
particle: $H(t)\equiv -\Delta + V(t)$, on $L^2({\mathbb
R}^n)$, in the so called repulsive case. We also show how to extend this result to other perturbations, including some nonlinear ones. |
|