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.
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     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/}
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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/