A quantum mechanical study of a simple two-dimensional problem identifies lines in coordinate space about which the probability densities are localised. These lines in general do not correspond to extrema in the system's static potential energy surface. The subject of this study has been the hydrogen atom in externally applied parallel electric and magnetic and magnetic fields. Probability density plots of eigenstates, in which the electron experiences comparable influences from all three fields: Coulomb, electric and magnetic, are each found to display a localisation at a polar angle related to an invariant previously obtained in a classical study of the problem. The line about which localisation occurs is found to vary with energy and is in coincidence with a periodic trajectory found within a classical framework.A quantum mechanical study of a simple two-dimensional problem identifies lines in coordinate space about which the probability densities are localised. These lines in general do not correspond to extrema in the system's static potential energy surface. The subject of this study has been the hydrogen atom in externally applied parallel electric and magnetic and magnetic fields. Probability density plots of eigenstates, in which the electron experiences comparable influences from all three fields: Coulomb, electric and magnetic, are each found to display a localisation at a polar angle related to an invariant previously obtained in a classical study of the problem. The line about which localisation occurs is found to vary with energy and is in coincidence with a periodic trajectory found within a classical framework.

Journal of Physics B Atomic Molecular and Optical PhysicsOct 28, 198811 citations

Hydrogen Atom Wave Functions

Elsevier eBooksJan 1, 19570 citations

Antihydrogen atom in external electric and magnetic fields

Leonti N Labzowsky, V. Sharipov

A theoretical comparison of the behavior of the antihydrogen $(\overline{\mathrm{H}})$ and hydrogen $(\mathrm{H})$ atoms in external electric and magnetic fields is made. It is shown that observable differences arise in the spectroscopic properties of $\mathrm{H}$ and $\overline{\mathrm{H}}$ atoms in parallel electric and magnetic fields of the order of 475 V∕cm and 0.12 T, respectively.A theoretical comparison of the behavior of the antihydrogen $(\overline{\mathrm{H}})$ and hydrogen $(\mathrm{H})$ atoms in external electric and magnetic fields is made. It is shown that observable differences arise in the spectroscopic properties of $\mathrm{H}$ and $\overline{\mathrm{H}}$ atoms in parallel electric and magnetic fields of the order of 475 V∕cm and 0.12 T, respectively.

Physical Review AJan 4, 20053 citations

Quantum Deformation of the Two-Dimensional Hydrogen Atom in a Magnetic Field

Anjana Sinha

International Journal of Theoretical PhysicsJul 1, 19981 citation

Experimentally attainable example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields

Dominique Delande, Jakub Zakrzewski

Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel, uniform, static electric, and magnetic fields, where tunneling is followed by ionization along the fields direction. Depending on the magnetic quantum number, one may observe either a standard Porter-Thomas distribution of tunneling rates or, for strong scarring by a periodic orbit parallel to the external fields, strong deviations from it. For the latter case, a simple model based on random matrix theory gives the correct distribution.Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel, uniform, static electric, and magnetic fields, where tunneling is followed by ionization along the fields direction. Depending on the magnetic quantum number, one may observe either a standard Porter-Thomas distribution of tunneling rates or, for strong scarring by a periodic orbit parallel to the external fields, strong deviations from it. For the latter case, a simple model based on random matrix theory gives the correct distribution.

arXiv:nlin/0307038Physical Review ADec 24, 200313 citations

A theoretical comparison of the behavior of the antihydrogen

(\overline{\mathrm{H}})

and hydrogen

(\mathrm{H})

atoms in external electric and magnetic fields is made. It is shown that observable differences arise in the spectroscopic properties of

\mathrm{H}

and

\overline{\mathrm{H}}

atoms in parallel electric and magnetic fields of the order of 475 V∕cm and 0.12 T, respectively.