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Green’s Function for the Quartic Oscillator

DOI: 10.4236/am.2016.714135, PP. 1571-1579

Keywords: Nonrelativistic, Quartic, Quantum, Mechanics, Green’s, Oscillator

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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.


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[2]  Anderson, R.L. (2013) Integration of the Classical Action for the Quartic Oscillator in 1+1 Dimensions. Applied Mathematics, 4, 117-122.
[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.
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