### Abstract

A concept of semiclassically concentrated states is developed on the basis of the Maslov germ theory. Higher approximations of semiclassical trajectory-coherent states and of semiclassical Green function (in the class of semiclassically concentrated states) for a many-dimensional Schrödinger-type equation are constructed. It is shown that, in class of such semiclassically concentrated states, a Schrödinger-type equation (up to any order of ℏ, ℏ → 0) is equivalent, from the viewpoint of calculating the quantum averages, to a closed finite system of ordinary differential equations.

Original language | English |
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Pages (from-to) | 231-290 |

Number of pages | 60 |

Journal | Annals of Physics |

Volume | 246 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Mar 1996 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Semiclassical trajectory-coherent approximation in quantum mechanics I. High-order corrections to multidimensional time-dependent equations of Schrödinger type.** / Bagrov, V. G.; Belov, V. V.; Trifonov, A. Yu.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 246, no. 2, pp. 231-290. https://doi.org/10.1006/aphy.1996.0027

}

TY - JOUR

T1 - Semiclassical trajectory-coherent approximation in quantum mechanics I. High-order corrections to multidimensional time-dependent equations of Schrödinger type

AU - Bagrov, V. G.

AU - Belov, V. V.

AU - Trifonov, A. Yu

PY - 1996/3/15

Y1 - 1996/3/15

N2 - A concept of semiclassically concentrated states is developed on the basis of the Maslov germ theory. Higher approximations of semiclassical trajectory-coherent states and of semiclassical Green function (in the class of semiclassically concentrated states) for a many-dimensional Schrödinger-type equation are constructed. It is shown that, in class of such semiclassically concentrated states, a Schrödinger-type equation (up to any order of ℏ, ℏ → 0) is equivalent, from the viewpoint of calculating the quantum averages, to a closed finite system of ordinary differential equations.

AB - A concept of semiclassically concentrated states is developed on the basis of the Maslov germ theory. Higher approximations of semiclassical trajectory-coherent states and of semiclassical Green function (in the class of semiclassically concentrated states) for a many-dimensional Schrödinger-type equation are constructed. It is shown that, in class of such semiclassically concentrated states, a Schrödinger-type equation (up to any order of ℏ, ℏ → 0) is equivalent, from the viewpoint of calculating the quantum averages, to a closed finite system of ordinary differential equations.

UR - http://www.scopus.com/inward/record.url?scp=0039075012&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039075012&partnerID=8YFLogxK

U2 - 10.1006/aphy.1996.0027

DO - 10.1006/aphy.1996.0027

M3 - Article

VL - 246

SP - 231

EP - 290

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 2

ER -