Probabilistic representation and fall-off of bound states of relativistic Schrodinger operators with spin 1/2
Fumio Hiroshima
Takashi Ichinose
Jozsef Lorinczi
2134/21512
https://repository.lboro.ac.uk/articles/journal_contribution/Probabilistic_representation_and_fall-off_of_bound_states_of_relativistic_Schrodinger_operators_with_spin_1_2/9384743
A Feynman-Kac type formula of relativistic Schrodinger operators with unbounded
vector potential and spin 1/2 is given in terms of a three-component process consisting
of Brownian motion, a Poisson process and a subordinator. This formula is
obtained for unbounded magnetic fields and magnetic fields with zeros. From this
formula an energy comparison inequality is derived. Spatial decay of bound states
is established separately for growing and decaying potentials by using martingale
methods.
2016-06-07 13:55:54
Relativistic Schrodinger operators
Bound states
Spatial decay
Feynman-Kac formulae
Poisson process
Subordinate Brownian motion
Martingales
Mathematical Sciences not elsewhere classified