Solution of spectral problem for Schr\"odinger equation with degenerate polinomial potential of even power
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 1, pp. 107-123
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The symmetry of the stationary Schrödinger equation with a degenerate potential
$U(x)=x^{2r}$, $r \in Z_+$, describing phase transitions in quantum systems, is reveled.
The analytical procedure of finding the eigenvalues of the potentials in question is constructed and realized numerically for $r=2,3,\dots,18$. The low energy levels are found.
@article{TMF_1996_109_1_a9,
author = {V. N. Sorokin and A. S. Vshivtsev and N. V. Norin},
title = {Solution of spectral problem for {Schr\"odinger} equation with degenerate polinomial potential of even power},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {107--123},
publisher = {mathdoc},
volume = {109},
number = {1},
year = {1996},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a9/}
}
TY - JOUR AU - V. N. Sorokin AU - A. S. Vshivtsev AU - N. V. Norin TI - Solution of spectral problem for Schr\"odinger equation with degenerate polinomial potential of even power JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1996 SP - 107 EP - 123 VL - 109 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a9/ LA - ru ID - TMF_1996_109_1_a9 ER -
%0 Journal Article %A V. N. Sorokin %A A. S. Vshivtsev %A N. V. Norin %T Solution of spectral problem for Schr\"odinger equation with degenerate polinomial potential of even power %J Teoretičeskaâ i matematičeskaâ fizika %D 1996 %P 107-123 %V 109 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a9/ %G ru %F TMF_1996_109_1_a9
V. N. Sorokin; A. S. Vshivtsev; N. V. Norin. Solution of spectral problem for Schr\"odinger equation with degenerate polinomial potential of even power. Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 1, pp. 107-123. http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a9/