A summation method for the Rayleigh-Schrödinger series for the anharmonic oscillator

Leonid Friedlander

doi:10.1063/1.526556

A summation method for the Rayleigh-Schrödinger series for the anharmonic oscillator

Leonid Friedlander

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We approximate the energy levels of the anharmonic oscillator with any coupling constant by eigenvalues λ_j(g,T) of the operator - d²/dx² + x² + gV_T(x) with V _T(x) = x⁴ when |x|≤T and V_T(x) = T ⁴ when |x| > T. The functions λ_j(g,T) are holomorphic with respect to g in a neighborhood of the non-negative half-axis. The conformal transformation maps this neighborhood onto the unit circle of the complex plane. It gives the summation method for the Rayleigh-Schrödinger series for every g>0.

Original language	English (US)
Pages (from-to)	961-964
Number of pages	4
Journal	Journal of Mathematical Physics
Volume	26
Issue number	5
DOIs	https://doi.org/10.1063/1.526556
State	Published - 1985
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.526556

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abstract = "We approximate the energy levels of the anharmonic oscillator with any coupling constant by eigenvalues λj(g,T) of the operator - d2/dx2 + x2 + gVT(x) with V T(x) = x4 when |x|≤T and VT(x) = T 4 when |x| > T. The functions λj(g,T) are holomorphic with respect to g in a neighborhood of the non-negative half-axis. The conformal transformation maps this neighborhood onto the unit circle of the complex plane. It gives the summation method for the Rayleigh-Schr{\"o}dinger series for every g>0.",

author = "Leonid Friedlander",

year = "1985",

doi = "10.1063/1.526556",

language = "English (US)",

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journal = "Journal of Mathematical Physics",

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N2 - We approximate the energy levels of the anharmonic oscillator with any coupling constant by eigenvalues λj(g,T) of the operator - d2/dx2 + x2 + gVT(x) with V T(x) = x4 when |x|≤T and VT(x) = T 4 when |x| > T. The functions λj(g,T) are holomorphic with respect to g in a neighborhood of the non-negative half-axis. The conformal transformation maps this neighborhood onto the unit circle of the complex plane. It gives the summation method for the Rayleigh-Schrödinger series for every g>0.

AB - We approximate the energy levels of the anharmonic oscillator with any coupling constant by eigenvalues λj(g,T) of the operator - d2/dx2 + x2 + gVT(x) with V T(x) = x4 when |x|≤T and VT(x) = T 4 when |x| > T. The functions λj(g,T) are holomorphic with respect to g in a neighborhood of the non-negative half-axis. The conformal transformation maps this neighborhood onto the unit circle of the complex plane. It gives the summation method for the Rayleigh-Schrödinger series for every g>0.

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JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 5

ER -

A summation method for the Rayleigh-Schrödinger series for the anharmonic oscillator

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