Convergence of scaled delta expansion: Anharmonic oscillator

Journal Article · Sat Jul 01 04:00:00 EDT 1995 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1995.1059· OSTI ID:165577

Guida, R; Konishi, K ^[1]; Suzuki, H ^[2]

---

1. Dipartimento di Fisica, Universita di Genoa, Via Dodecaneso, 33-16146 Genoa (Italy)
2. Istituto Nazionale di Fisica Nucleare, sez. di Genova, Via Dodecaneso, 33-16146 Genoa (Italy)

We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency {Omega} is chosen to scale with the order as {Omega}={ital CN}{sup {gamma}}; 1/3{lt}{gamma}{lt}1/2, {ital C}{gt}0 as {ital N} {r_arrow} {infinity}. It converges also for {gamma}=1/3, if {ital C}{ge}{alpha}{sub {ital c}} {ital g}{sup 1/3}, {alpha}{sub {ital c}}{congruent}0.570875, where {ital g} is the coupling constant in front of the operator {ital q}{sup 4}/4. The extreme case with {gamma}=1/3, {ital C}={alpha}{sub {ital c}} {ital g}{sup 1/3} corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones. {copyright} 1995 Academic Press, Inc.

• OSTI ID: 165577
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 241; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANHARMONIC OSCILLATORS
CONVERGENCE
ENERGY LEVELS
PERTURBATION THEORY
QUANTUM MECHANICS
SERIES EXPANSION