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.
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
![\"\"](\"Edit_dfd9fb44-382f-4666-af63-0121aea44aec.bmp\")
？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 ![\"\"](\"Edit_48a3fe65-700f-484d-b650-df50c98a4553.bmp\")
？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.
