dorsal/arxiv
View SchemaElectron bound by a potential well in the presence of a constant uniform magnetic field
| Authors | V. R. Khalilov, F. Kh. Chibirova |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702218 |
| URL | https://arxiv.org/abs/quant-ph/0702218 |
| DOI | 10.1088/1751-8113/40/24/013 |
Abstract
We study the effect of a constant uniform magnetic field on an electrically charged massive particle (an electron) bound by a potential well, which is described by means of a single attractive $\lambda\delta({\bf r})$ potential. A transcendental equation that determines the electron energy spectrum is derived and solved. The electron wave function in the ground (bound) state is approximately constructed in a remarkable simple form. It is shown that there arises the probability current in the bound state in the presence of a uniform constant magnetic field. This (electric) current, being by the gauge invariant quantity, must be observable and involve (and exercise influence on) the electron scattering. The probability current density resembles a stack of "pancake" vortices'' whose circulating "currents'' around the magnetic field direction ($z$-axes) are mostly confined within the plane $z=0$. We also compute the tunnelling probability of electron from the bound to free state under a weak constant homogeneous electric field, which is parallel to the magnetic field. The model under consideration is briefly discussed in two spatial dimensions.
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"abstract": "We study the effect of a constant uniform magnetic field on an electrically\ncharged massive particle (an electron) bound by a potential well, which is\ndescribed by means of a single attractive $\\lambda\\delta({\\bf r})$ potential. A\ntranscendental equation that determines the electron energy spectrum is derived\nand solved. The electron wave function in the ground (bound) state is\napproximately constructed in a remarkable simple form. It is shown that there\narises the probability current in the bound state in the presence of a uniform\nconstant magnetic field. This (electric) current, being by the gauge invariant\nquantity, must be observable and involve (and exercise influence on) the\nelectron scattering. The probability current density resembles a stack of\n\"pancake\" vortices\u0027\u0027 whose circulating \"currents\u0027\u0027 around the magnetic field\ndirection ($z$-axes) are mostly confined within the plane $z=0$. We also\ncompute the tunnelling probability of electron from the bound to free state\nunder a weak constant homogeneous electric field, which is parallel to the\nmagnetic field. The model under consideration is briefly discussed in two\nspatial dimensions.",
"arxiv_id": "quant-ph/0702218",
"authors": [
"V. R. Khalilov",
"F. Kh. Chibirova"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1751-8113/40/24/013",
"title": "Electron bound by a potential well in the presence of a constant uniform magnetic field",
"url": "https://arxiv.org/abs/quant-ph/0702218"
},
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