ENERGY-SPECTRUM OF THE POTENTIAL V = AX2 + X4

Suitable sequences of quasi-exactly solvable Hamiltonians are shown to provide stringent upper bounds to the energy eigenvalues of the bound state potential V = ax2 + x4. Procedures to convert these bounds into even further improved energy estimates are developed. For the quartic anharmonic oscillator (a > 0) case a simple argument is provided to indicate that the conventional small-parameter energy expansion does not converge as a Taylor series. An accurate closed-form parametrization of the entire quartic (a = 0) spectrum is noted. The energy difference between the lowest-lying levels of a quartic double well (a < 0) is satisfactorily recovered and for deep wells a useful expression is deduced for it empirically.

Authors
CHHAJLANY S.C. , LETOV D.A. , MALNEV V.N.
Number of issue
12
Language
English
Pages
2731-2741
Status
Published
Volume
24
Year
1991
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/9742/
Share

Other records

KUZNETSOV V.V., PALMA A.R., ALIEV A.E., VARLAMOV A.V., PROSTAKOV N.S.
ZHURNAL ORGANICHESKOI KHIMII. MEZHDUNARODNAYA KNIGA / Санкт-Петербургская издательская фирма "Наука" Академиздатцентра РАН. Vol. 27. 1991. P. 1579-1581