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 |
|---|---|
| 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.
In: Annals of Physics, Vol. 246, No. 2, 15.03.1996, p. 231-290.Research output: Contribution to journal › Article
}
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
AN - SCOPUS:0039075012
VL - 246
SP - 231
EP - 290
JO - Annals of Physics
JF - Annals of Physics
SN - 0003-4916
IS - 2
ER -