# Probabilistic representation and fall-off of bound states of relativistic Schrödinger operators with spin 1/2

Fumio Hiroshima, Takashi Ichinose, József Lorinczi

9 引用 (Scopus)

### 抄録

A Feynman-Kac type formula for relativistic Schrödinger operators with unbounded vector potential and spin 1=2 is given in terms of a three-component process consisting of a 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 for decaying potentials by using martingale methods.

元の言語 英語 189-214 26 Publications of the Research Institute for Mathematical Sciences 49 1 https://doi.org/10.4171/PRIMS/102 出版済み - 5 16 2013

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Bound States
Operator
Magnetic Field
Martingale Method
Subordinator
Vector Potential
Poisson process
Brownian motion
Decay
Zero
Energy

### All Science Journal Classification (ASJC) codes

• Mathematics(all)

### これを引用

Probabilistic representation and fall-off of bound states of relativistic Schrödinger operators with spin 1/2. / Hiroshima, Fumio; Ichinose, Takashi; Lorinczi, József.

：: Publications of the Research Institute for Mathematical Sciences, 巻 49, 番号 1, 16.05.2013, p. 189-214.

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