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 AM  Vol.7 No.14 , August 2016
Green’s Function for the Quartic Oscillator
Abstract: In this paper, a quantum mechanical Green’s function  for the quartic oscillator is presented. This result is built upon two previous papers: first [1], detailing the linearization of the quartic oscillator (qo) to the harmonic oscillator (ho); second [2], the integration of the classical action function for the quartic oscillator. Here an equivalent form for the quartic oscillator action function  in terms of harmonic oscillator variables is derived in order to facilitate the derivation of the quartic oscillator Green’s Function, namely in fixing its amplitude.
Cite this paper: Anderson, R. (2016) Green’s Function for the Quartic Oscillator. Applied Mathematics, 7, 1571-1579. doi: 10.4236/am.2016.714135.
References

[1]   Anderson, R.L. (2010) An Invertible Linearization Map for the Quartic Oscillator. Journal of Mathematical Physics, 51, Article ID: 122904.
http://dx.doi.org/10.1063/1.3527070

[2]   Anderson, R.L. (2013) Integration of the Classical Action for the Quartic Oscillator in 1+1 Dimensions. Applied Mathematics, 4, 117-122.
http://dx.doi.org/10.4236/am.2013.410A3014

[3]   Schiff, L.I. (1955/1968) Quantum Mechanics. 3rd Edition, McGraw-Hill, New York, p. 306.

[4]   Dirac, P.A.M. (1958) The Principle of Quantum Mechanics. 4th Edition, Oxford at the Clarendon Press, p. 128.

[5]   Brown, L.M. (Ed.) (2005) Feynman’s Thesis—A New Approach to Quantum Theory. World Scientific, Singapore.

[6]   Feynman, R.P. and Hibbs, A.R. (1965) Quantum Mechanics and Path Integrals. McGraw-Hill, New York.

[7]   Santos, R.C., Santos, J. and Lima, J.A.S. (2006) Hamilton-Jacobi Approach for Power-Law Potentials. Brazilian Journal of Physics, 36, 1257-1261.
http://dx.doi.org/10.1590/S0103-97332006000700024

 
 
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