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 = CNgamma; 1/3 < gamma < 1/2, C > 0 as N --> infinity. It converges also for gamma = 1/3, if C greater than or equal to alpha(c)g(1/3), alpha(c) similar or equal to 0.570875, where g is the coupling constant in front of the operator q(4)/4. The extreme case with gamma = 1/3, C = x(c) g(1/3) corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones. (C) 1995 Academic Press, Inc.
CONVERGENCE OF SCALED DELTA-EXPANSION - ANHARMONIC-OSCILLATOR
KONISHI, KENICHI;
1995-01-01
Abstract
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 = CNgamma; 1/3 < gamma < 1/2, C > 0 as N --> infinity. It converges also for gamma = 1/3, if C greater than or equal to alpha(c)g(1/3), alpha(c) similar or equal to 0.570875, where g is the coupling constant in front of the operator q(4)/4. The extreme case with gamma = 1/3, C = x(c) g(1/3) corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones. (C) 1995 Academic Press, Inc.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
