کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1856652 | 1529885 | 2012 | 18 صفحه PDF | دانلود رایگان |

In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states localized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge–Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r1/r potential.
► The spectrum of confined electrons and self-adjoint extension parameter.
► Cavity resonances between hydrogen bound states and states localized at the wall.
► Accidental symmetry for hydrogen atom confined in a sphere or on a cone.
Journal: Annals of Physics - Volume 327, Issue 11, November 2012, Pages 2742–2759