We study a non-relativistic charged quantum particle moving in a bounded open set $\Omega\subset\R^3$ with smooth boundary under the action of a zero-range potential. In the electrostatic case the standing wave solution takes the form $\psi(t,x)=u(x)e^{-i\omega t}$ where $u$ formally satisfies $-\Delta u+\alpha\varphi u-\frac1{\beta}\delta_{x_0} u=\omega u$ and the electric potential $\varphi$ is given by $-\Delta\varphi = u^2$. We give a rigorous definition of this problem and show that it has a weak nontrivial solution.
The Schrodinger-Maxwell system with Dirac mass / Coclite, Giuseppe Maria; Holden, H.. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 24:5(2007), pp. 773-793. [10.1016/j.anihpc.2006.06.005]
The Schrodinger-Maxwell system with Dirac mass
COCLITE, Giuseppe Maria;
2007-01-01
Abstract
We study a non-relativistic charged quantum particle moving in a bounded open set $\Omega\subset\R^3$ with smooth boundary under the action of a zero-range potential. In the electrostatic case the standing wave solution takes the form $\psi(t,x)=u(x)e^{-i\omega t}$ where $u$ formally satisfies $-\Delta u+\alpha\varphi u-\frac1{\beta}\delta_{x_0} u=\omega u$ and the electric potential $\varphi$ is given by $-\Delta\varphi = u^2$. We give a rigorous definition of this problem and show that it has a weak nontrivial solution.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
