The time slicing approximation of the fundamental solution for the Schrödinger equation with electromagnetic fields

Daisuke FUJIWARA; Tetsuo TSUCHIDA

doi:10.2969/jmsj/04920299

Daisuke FUJIWARA, Tetsuo TSUCHIDA

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 2 Pages 299-327

DOI https://doi.org/10.2969/jmsj/04920299

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Published: 1997 Received: May 02, 1995 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) K, Asada and D, Fujiwara, On some oscillatory integral transformations in L²(Rⁿ), Japan. J. Math., 4 (1978), 299-361.
2) R. P. Feynman, Space time approach to non-relativistic quantum mechanics, Rev. Modern Phys., 20 (1948), 367-386.
3) D. Fujiwara, A construction of the fundamental solution for the Schrödinger equation, J. Analyse Math., 35 (1979), 41-96.
4) D. Fujiwara, Remarks on convergence of some Feynman path integrals, Duke Math. J., 47 (1980), 559-600.
5) D. Fujiwara, A remark on Taniguchi-Kumanogo theorem for product of Fourier integral operators, Pseudo-differential operators, Proc. Oberwolfach 1986, Lecture Notes in Math., 1256, Springer, 1987, pp. 135-153.
6) D. Fujiwara, The stationary phase method with an estimate of the remainder term on a space of large dimension, Nagoya Math. J., 124 (1991), 61-97.
7) D. Fujiwara, Some Feynman path integrals as oscillatory integrals over a Sobolev manifold, Lecture Notes in Math., 1540, Springer, 1993, pp. 39-53.
8) D. Fujiwara, Some Feynman path integrals as oscillatory integrals over a Sobolev manifold, preprint, January 1993.
9) H. Kitada, On a construction of the fundamental solution for Schrödinger equations, J. Fac. Sci. Univ. Tokyo Sec. IA, 27 (1980), 193-226.
10) B. Simon, Trace ideals and their applications, London Math. Soc. Lecture Note Ser., 35, Cambridge Univ. Press, Cambridge, 1979.
11) T. Tsuchida, Remarks on Fujiwara's stationary phase method on a space of large dimension with a phase function involving electromagnetic fields, Nagoya Math. J., 136 (1994), 157-189.
12) K. Yajima, Schrödinger evolution equations with magnetic fields, J. Analyse Math., 56 (1991), 29-76.

Right : [1] K. Asada and D. Fujiwara, On some oscillatory integral transformations in L²(Rⁿ), Japan. J. Math., 4 (1978), 299-361.
[2] R. P. Feynman, Space time approach to non-relativistic quantum mechanics, Rev. Modern Phys., 20 (1948), 367-386.
[3] D. Fujiwara, A construction of the fundamental solution for the Schrödinger equation, J. Analyse Math., 35 (1979), 41-96.
[4] D. Fujiwara, Remarks on convergence of some Feynman path integrals, Duke Math. J., 47 (1980), 559-600.
[5] D. Fujiwara, A remark on Taniguchi-Kumanogo theorem for product of Fourier integral operators, Pseudo-differential operators, Proc. Oberwolfach 1986, Lecture Notes in Math., 1256, Springer, 1987, pp. 135-153.
[6] D. Fujiwara, The stationary phase method with an estimate of the remainder term on a space of large dimension, Nagoya Math. J., 124 (1991), 61-97.
[7] D. Fujiwara, Some Feynman path integrals as oscillatory integrals over a Sobolev manifold, Lecture Notes in Math., 1540, Springer, 1993, pp. 39-53.
[8] D. Fujiwara, Some Feynman path integrals as oscillatory integrals over a Sobolev manifold, preprint, January 1993.
[9] H. Kitada, On a construction of the fundamental solution for Schrödinger equations, J. Fac. Sci. Univ. Tokyo Sec. IA, 27 (1980), 193-226.
[10] B. Simon, Trace ideals and their applications, London Math. Soc. Lecture Note Ser., 35, Cambridge Univ. Press, Cambridge, 1979.
[11] T. Tsuchida, Remarks on Fujiwara's stationary phase method on a space of large dimension with a phase function involving electromagnetic fields, Nagoya Math. J., 136 (1994), 157-189.
[12] K. Yajima, Schrödinger evolution equations with magnetic fields, J. Analyse Math., 56 (1991), 29-76.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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