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Propagators from integral representations of Green’s functions for the N‐dimensional free‐particle, harmonic oscillator and Coulomb problems
dc.contributor.authorBlinder, S. M.en_US
dc.date.accessioned2010-05-06T23:28:23Z
dc.date.available2010-05-06T23:28:23Z
dc.date.issued1984-04en_US
dc.identifier.citationBlinder, S. M. (1984). "Propagators from integral representations of Green’s functions for the N‐dimensional free‐particle, harmonic oscillator and Coulomb problems." Journal of Mathematical Physics 25(4): 905-909. <http://hdl.handle.net/2027.42/71268>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/71268
dc.description.abstractThe radial Green’s functions for the N‐dimensional free‐particle, isotropic harmonic oscillator and Coulomb problems all contain a product of two Bessel or Whittaker functions. After integral representations for these respective products are introduced, each Green’s function exhibits the structure of a Fourier transform. One obtains thereby the Feynman propagators K(r1,r2,t) for the free particle and harmonic oscillator. In the Coulomb case, the Fourier transform involves the quantum number variable and leads instead to the recently defined Sturmian propagator. The well‐known connection between Coulomb and oscillator eigenstates of various dimensionality is manifested in a new way by the structure of the propagators derived here.en_US
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dc.format.extent285809 bytes
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dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titlePropagators from integral representations of Green’s functions for the N‐dimensional free‐particle, harmonic oscillator and Coulomb problemsen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Chemistry, University of Michigan, Ann Arbor, Michigan 48109en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/71268/2/JMAPAQ-25-4-905-1.pdf
dc.identifier.doi10.1063/1.526245en_US
dc.identifier.sourceJournal of Mathematical Physicsen_US
dc.identifier.citedreferenceThe form of the N‐dimensional Laplacian is given by J. D. Louck, J. Mol. Spectrosc. 4, 298 (1960).en_US
dc.identifier.citedreferenceSee, for example, S. I. Vetchinkin and V. L. Bachrach, Int. J. Quantum Chem. 6, 143 (1972).en_US
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dc.identifier.citedreferenceReference 4, p. 361, Eq. (9.1.30).en_US
dc.identifier.citedreferenceReference 4, p. 362, Eq. (9.1.69).en_US
dc.identifier.citedreferenceR. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw‐Hill, New York, 1965), p. 58ff; Ref. 3, p. 152.en_US
dc.identifier.citedreferenceReference 4, p. 440, Eq. (10.1.47).en_US
dc.identifier.citedreferenceReference 3, p. 155, Eq. (6.5.56).en_US
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dc.identifier.citedreferenceReference 11, p. 25, Eq. (33).en_US
dc.identifier.citedreferenceReference 11, p. 86, Eq. (5c).en_US
dc.identifier.citedreferenceReference 8, p. 63, Eq. (3.59); Ref. 3, p. 11, Eq. (1.4.29).en_US
dc.identifier.citedreferenceReference 11, p. 139, Eq. (12a).en_US
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dc.identifier.citedreferenceReference 11, p. 212.en_US
dc.identifier.citedreferenceA very similar formula for a harmonic oscillator perturbed by an inverse quadratic potential has been given by D. C. Khandekar and S. V. Lawande, J. Math. Phys. 16, 384 (1975).en_US
dc.identifier.citedreferenceReference 3, p. 159, Eq. (6.5.87).en_US
dc.identifier.citedreferenceReference 11, with z  =  r,λ  =  1,β  = (1−N)/2,A  =  −2ik,κ  =  iZ/k,μ/2  =  L+N/2−1.z=r,λ=1,β=(1−N)∕2,A=−2ik,κ=iZ∕k,μ∕2=L+N∕2−1.en_US
dc.identifier.citedreferenceL. C. Hostler, J. Math. Phys. 11, 2966 (1970).en_US
dc.identifier.citedreferenceS. M. Blinder, “Sturmian propagator for the nonrelativistic Coulomb problem,” Phys. Rev. A (in press).en_US
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dc.identifier.citedreferenceE. Schrödinger, Proc. R. Irish Acad. A 46, 183 (1941).en_US
dc.identifier.citedreferenceA. Giovannini and T. Tonietti, Nuovo Cimento A 54, 1 (1968).en_US
dc.identifier.citedreferenceJ. Schwinger, unpublished lecture notes; see also G. Bahm, Lectures on Quantum Mechanics (Benjamin, Reading, MA, 1969), p. 179.en_US
dc.identifier.citedreferenceD. Bergmann and Y. Frishman, J. Math. Phys. 6, 1855 (1965).en_US
dc.identifier.citedreferenceReference 5, p. 140, Eq. (3) with v  =  0,μ  =  1,k  =  cos(θ/2),Pl(cos θ)  =  (−)2F11[−1,1+1;cos2(θ/2)].v=0,μ=1,k=cos(θ∕2),Pl(cosθ)=(−)2F11[−1,1+1;cos2(θ∕2)].en_US
dc.identifier.citedreferenceL. Hostler, J. Math. Phys. 5, 591 (1964).en_US
dc.owningcollnamePhysics, Department of


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