Étude probabiliste de l'opérateur de Schrödinger
Annales scientifiques de l'Université de Clermont. Mathématiques (1979)
- Volume: 67, Issue: 17, page 5-18
- ISSN: 0249-7042
Access Full Article
topHow to cite
topCarmona, René. "Étude probabiliste de l'opérateur de Schrödinger." Annales scientifiques de l'Université de Clermont. Mathématiques 67.17 (1979): 5-18. <http://eudml.org/doc/80485>.
@article{Carmona1979,
author = {Carmona, René},
journal = {Annales scientifiques de l'Université de Clermont. Mathématiques},
keywords = {Schrödinger Operator; Path Integrals; Spectral Properties; Exponential Decay of Eigenfunctions},
language = {fre},
number = {17},
pages = {5-18},
publisher = {UER de Sciences exactes et naturelles de l'Université de Clermont},
title = {Étude probabiliste de l'opérateur de Schrödinger},
url = {http://eudml.org/doc/80485},
volume = {67},
year = {1979},
}
TY - JOUR
AU - Carmona, René
TI - Étude probabiliste de l'opérateur de Schrödinger
JO - Annales scientifiques de l'Université de Clermont. Mathématiques
PY - 1979
PB - UER de Sciences exactes et naturelles de l'Université de Clermont
VL - 67
IS - 17
SP - 5
EP - 18
LA - fre
KW - Schrödinger Operator; Path Integrals; Spectral Properties; Exponential Decay of Eigenfunctions
UR - http://eudml.org/doc/80485
ER -
References
top- [1] S. Albeverio, R. Hoegh-Krohn and L. Streit - Energy Forms, Hamiltonians and Distorted Brownian Paths. J. Math. Phys.18 (1977) 907-917. Zbl0368.60091MR446236
- [2] D.W. Babbit - The Wiener Integral and Perturbation of the Schrödinger Operator. Bull. Amer. Math, Soc.70 (1964) 254-259. Zbl0196.44901MR161180
- [3] J.F. Barnes, H.J. Brascamp and E.H. Lieb - Lower Bound for the Ground State Energy of the Schrödinger Equation Using the Sharp Form of Young's Inequality. Studies in Math. Phys. Essays in Honour of V. Bargman. Princeton Univ. Press (1976). Zbl0354.35028
- [4] A.M. Berthier et B. Gaveau - Critère de convergence des fonctionnelles de Kac et application en mécanique quantique et en géometrie. J. Funct. Anal. (à paraître). Zbl0398.60076MR512253
- [5] R. Carmona - Regularity Properties of Schrödinger and Dirichlet Semigroups. J. Funct. Anal. (à paraître). Zbl0419.60075MR549115
- [6] R. Carmona - Pointwise Bounds for Schrödinger Eigenstates. Comm. Math. Phys.62 (1978) 97-106. Zbl0403.47016MR505706
- [7] P. Deift and B. Simon - On the Decoupling of Finite Singularities from the Question of Asymptotic Completeness in Two-Body Quantum Systems. J. Funct. Anal.23 (1976) 218-238. Zbl0344.47007MR432051
- [8] M.D. Donsker and S.R.S. Varadhan - Asymptotic Evaluation of Certain Wiener Integrals for Large Time. Proc. Int. Conf. on Function Space Integration. Zbl0333.60078
- [9] J.P. Eckmann - Hypercontractivity for Anharmonic Oscillators. J. Funct. Anal.16 (1974) 388-404. Zbl0285.47032MR372683
- [10] H. Ezawa, J.R. Klauder and L.A. Shepp - A Path Space Picture for Feynman - Kac averages. Ann. Phys.88 (1974) 588-620. Zbl0296.60074MR384018
- [11] H. Ezawa, J.R. Klauder and L.A. Shepp - Vestigial Effects of Singular Potentials in Diffusion Theory and Quantum Mechanics. J. Math. Phys.16 MR400982
- [12] W.G. Faris - Self-Adjoint Operators. Lect. Notes in Math.# 433 (1975). Springer-Verlag. Zbl0317.47016MR467348
- [13] W.G. Faris and B. Sinon - Degenerate and Non-Degenerate Ground States for Schrödinger Operators. Duke Math. J.42 (1975) 559-567. Zbl0339.35033MR381571
- [14] J. Feldman - On the Schrödinger and Heat Equations for Non-Negative Potentials. Trans. Amer. Math. Soc.108 (1963) 251-264. Zbl0116.07302MR160264
- [15] J. Ginibre - Some Applications of Functional Integration in Statistical Mechanics. Dans "Statistical Mechanics and Quantum Field Theory" (C. De Witt et R. Stora Edts.) p. 327-427. Gordon and Breach - New York (1970).
- [16] L. Gross - Logarithmic Sobolev Inequalities. Amer. J. Math.97 (1976) 1061-1083. Zbl0318.46049MR420249
- [17] I.W. Herbst and A.D. Sloan - Perturbation of Translation Invariant Positivity Preserving Semi-groups on L2(Rn). Trans. Amer. Math. Soc.236 (1978) 238-360. Zbl0388.47022MR470750
- [18] R. Hoegh-Krohn and B. Simon - Hypercontractive Semigroups and Two Dimensional Bose Fields. J. Funct. Anal.9 (1972) 121-180. Zbl0241.47029MR293451
- [19] K. Ito and H.P. McKean - Diffusion Processes and their Sample Paths. Springer-Verlag (1974) 2nd Printing. Zbl0285.60063MR345224
- [20] M. Kac - On some Connection between Probability Theory and Differential and Integral Equations. Proc. 2nd Berk. Symp. on Math. Stat. and Prob. (1951) 189-215. Zbl0045.07002MR45333
- [21] T. Kato - Perturbation Theory for Linear Operators. Springer-Verlag (1966). Zbl0148.12601MR203473
- [22] E.H. Lieb - Bounds on the Eigenvalues of the Laplace and Schrödinger Operators. Bull. Amer. Math. Soc.82 (1976) 751-753. Zbl0329.35018MR407909
- [23] H P.McKEAN- -Δ plus a bad potential. J. Math. Phys.18 (1977) 1277-1279. Zbl0357.47025
- [24] E. Nelson - The Free Markov Field. J. Funct. Anal.13 (1973) 211-227. Zbl0273.60079MR343816
- [25] J. Neveu - Sur l'esperance conditionnelle par rapport à un mouvement brownien. Ann. Inst. H. Poincaré. Sect.B. 12 (1976) 105-109. Zbl0356.60028MR431400
- [26] N.I. Portenko - Diffusion Processes with Unbounded Drift Coefficient. Theor. Prob. Appl.20 (1975) 27-37. Zbl0335.60050MR375483
- [27] D. Ray - On the Spectra of Second Order Differential Operators. Trans. Amer. Math. Soc.77 (1954) 299-321. Zbl0058.32901MR66539
- [28] M. Reed and B. Sinon - Methods of Modern Mathematical Physics, I. Functional Analysis (1972) II. Fourier Analysis and Self-Adjointness (1975) IV. Analysis of Operators (1978) Academic Press. Zbl0242.46001MR493419
- [29] J.S. Rosen - Sobolev Inequalities for Weight Spaces and Supercontractivity. Trans. Amer. Math. Soc.222 (1976) 367-376. Zbl0344.46072MR425601
- [30] Yu. A. Semenov - Schrödinger Operators with Llocp - Potentials. Comm. Math . Phys.53 (1977) 277-284, Zbl0346.47011MR473920
- [31] B. Simon - Quantum Mechanics for Hamiltonians Defined as Quadratic Forms. Princeton Series in Physics. (1971) Princeton Univ. Press. Zbl0232.47053MR455975
- [32] B. Simon - The P(Ø)2 Euclidean Field Theory. Princeton Series in Physics. (1973) Princeton Univ. Press. MR489552
- [33] B. Simon - Pointwise Bounds on Eigenfunctions and Wave-Packets in N.Body Quantum Systems. II. Proc. Amer. Math. Soc.45 (1974) 454-456 III. Trans. Amer. Math. Soc.208 (1975) 317-329. Zbl0292.35061MR417597
- [34] B. Simon - Functional Integration and Quantum Physics. Academic Press. New York (à paraître). Zbl0434.28013MR544188
- [35] J.E. Snol - On the Behaviour of the Eigenfunctions of Schrödinger's Equation, Mat. Sb.46 (1957) 273-286. (Russe). Zbl0078.27904MR125315
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.