### Abstract

The modification of the Bohr-Sommerfeld quantization rules, which is due to the barrier penetrability, is found. The equation obtained is valid for an arbitrary analytical potential U(x), obeying the quasiclassical conditions. It determines both the position E_{r} and the width Δ of the quasistationary state. A generalization of the Gamow formula for multidimensional systems with separable coordinates is derived. A comparison with exactly solvable models as well as with numerical solutions of the Schrödinger equation for the Stark problem is performed.

Original language | English |
---|---|

Pages (from-to) | 185-191 |

Number of pages | 7 |

Journal | Physics Letters A |

Volume | 157 |

Issue number | 4-5 |

DOIs | |

Publication status | Published - 29 Jul 1991 |

Externally published | Yes |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters A*,

*157*(4-5), 185-191. https://doi.org/10.1016/0375-9601(91)90048-D

**Quantization rules for quasistationary states.** / Popov, V. S.; Mur, V. D.; Sergeev, A. V.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 157, no. 4-5, pp. 185-191. https://doi.org/10.1016/0375-9601(91)90048-D

}

TY - JOUR

T1 - Quantization rules for quasistationary states

AU - Popov, V. S.

AU - Mur, V. D.

AU - Sergeev, A. V.

PY - 1991/7/29

Y1 - 1991/7/29

N2 - The modification of the Bohr-Sommerfeld quantization rules, which is due to the barrier penetrability, is found. The equation obtained is valid for an arbitrary analytical potential U(x), obeying the quasiclassical conditions. It determines both the position Er and the width Δ of the quasistationary state. A generalization of the Gamow formula for multidimensional systems with separable coordinates is derived. A comparison with exactly solvable models as well as with numerical solutions of the Schrödinger equation for the Stark problem is performed.

AB - The modification of the Bohr-Sommerfeld quantization rules, which is due to the barrier penetrability, is found. The equation obtained is valid for an arbitrary analytical potential U(x), obeying the quasiclassical conditions. It determines both the position Er and the width Δ of the quasistationary state. A generalization of the Gamow formula for multidimensional systems with separable coordinates is derived. A comparison with exactly solvable models as well as with numerical solutions of the Schrödinger equation for the Stark problem is performed.

UR - http://www.scopus.com/inward/record.url?scp=0040145287&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040145287&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(91)90048-D

DO - 10.1016/0375-9601(91)90048-D

M3 - Article

AN - SCOPUS:0040145287

VL - 157

SP - 185

EP - 191

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 4-5

ER -