Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 85, 2006 - Issue 6-7
Submit an article Journal homepage
37
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Applying reproducing kernels to the evaluation and approximation of the simple and time-dependent imaginary time harmonic oscillator path integrals

Daniel Keren Department of Computer Science, Haifa University, Haifa 31905, IsraelCorrespondence[email protected]
Pages 793-810 | Received 08 Aug 2005, Accepted 29 Mar 2006, Published online: 28 Nov 2010

References

  • Feynman , RP and Hibbs , AR . 1965 . Quantum Mechanics and Path Integrals , New York : McGraw-Hill .
  • Grosche , S and Steiner , F . 1998 . Handbook of Feynman Path Integrals, Springer Tracts in Modern Physics , Vol. 145 , Berlin : Springer-Verlag .
  • Schulman , LS . 1981 . Techniques and Applications of Path Integration , New York : Wiley Interscience .
  • Saitoh , S , Matsuura , T and Asaduzzaman , M . 2003 . Operator equations and best approximation problems in reproducing kernel Hilbert spaces . Journal of Analysis and Applications , 1 ( 3 ) : 131 – 142 .
  • Larkin , FM . 1972 . Gaussian measure in Hilbert space and applications in numerical analysis . Rocky Mountain Journal of Mathematics , 2 : 379 – 421 .
  • Doll , JD , Coalson , RD and Freeman , DL . 1985 . Fourier path-integral Monte Carlo methods: partial averaging . Physical Review Letters , 55 : 1 – 4 .
  • Bond , SD , Laird , BB and Leimkuhler , BJ . 2003 . On the approximation of Feynman-Kac path integrals . Journal of Computational Physics , 185 : 472 – 483 .
  • Cruzeiro-Hansson , L , Baum , JO and Finney , JL . 1993 . Two modified staging algorithms for path integral Monte Carlo simulations . Journal of Computational Physics , 104 : 110 – 117 .
  • Doll , JD and Freeman , DL . 1984 . A Monte-Carlo method for quantum Boltzmann statistical mechanics . Journal of Chemical Physics , 80 : 2239 – 2240 .
  • Hetenyi , B , Rabani , E and Berne , BJ . 1999 . Path-integral diffusion Monte Carlo: calculation of observables of many-body systems in the ground state . Journal of Chemical Physics , 110 : 6143 – 6153 .
  • Plaskota , L , Wasilkowski , GW and Wozniakowski , H . 2000 . A new algorithm and worst case complexity for Feynman–Kac path integration . Journal of Computational Physics , 164 : 335 – 353 .
  • Predescu , C and Doll , JD . 2002 . Optimal series representations for numerical path integral simulations . Journal of Chemical Physics , 117 : 7448 – 7463 .
  • Predescu , C , Sabo , D and Doll , JD . 2003 . Numerical implementation of some reweighted path integral methods . Journal of Chemical Physics , 119 : 4641 – 4654 .
  • Guasti , MF and Moya-Cessa , H . 2003 . Solution of the Schrödinger equation for time-dependent 1D harmonic oscillators using the orthogonal functions invariant . Journal of Physics A , 36 : 2069 – 2076 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.