Paul, Thierry; Uribe, Alejandro A construction of quasi-modes using coherent states. (English) Zbl 0808.35118 Ann. Inst. Henri Poincaré, Phys. Théor. 59, No. 4, 357-381 (1993). Summary: We present a construction of semi-classical vectors satisfying the Schrödinger equation modulo \(\hslash^ \infty\). These vectors have nice regular properties, in particular they don’t have turning points. An application is given to the calculation of matrix elements. The present work is meant as an introduction to a more general theory which is announced. Cited in 16 Documents MSC: 35Q40 PDEs in connection with quantum mechanics 81R30 Coherent states Keywords:Schrödinger equation modulo \(\hslash^ \infty\) × Cite Format Result Cite Review PDF Full Text: Numdam EuDML References: [1] V. Bargman , On a Hilbert Space of Analytic Functions and an Associated Integral Transform, I. , Comm. Pure Appl. Math. , Vol. 14 , 1961 , pp. 187 - 214 . MR 157250 | Zbl 0107.09102 · Zbl 0107.09102 · doi:10.1002/cpa.3160140303 [2] V. Guillemin , Symplectic Spinors and Partial Differential Equations , Géométrie symplectique et Physique mathématique , J. M. SOURIAU Ed., C.N.R.S ., 1974 . MR 461591 [3] G.A. Hagedorn , Semiclassical Quantum Mechanics I. , Comm. Math. Phys. , Vol. 71 , 1980 , pp. 77 - 93 . Article | MR 556903 [4] L. Hormander , The Theory of Linear Differential Operators , Vol. 1 , Springer Verlag . [5] L.D. Landau and E.M. Lifshitz , Quantum Mechanics , Pergamon Press , 1977 . [6] R.G. Litteljohn , The Semiclassical Evolution of Wave Packets , Physics Reports , Vol. 138 , 1986 , pp. 193 - 291 . MR 845963 [7] T. Paul and A. Uribe , In preparation. [8] D. Robert , Autour de l’Approximation Semi-Classique , Birkhauser , 1987 . MR 897108 | Zbl 0621.35001 · Zbl 0621.35001 [9] M.A. Shubin , Pseudo-Differential Operators and Spectral Theory , Springer Verlag , 1987 . MR 883081 | Zbl 0616.47040 · Zbl 0616.47040 [10] A. Voros , Thèse , Université d’Orsay , 1977 (unpublished). [11] A. Voros , W.K.B. in the Bargman representation , Phys. Rev. A. , Vol. 40 , 1989 , pp. 6814 - 6825 . MR 1031937 [12] G. Foland , Harmonic Analysis on Phase Space , Annals of Mathematics Studies , Princeton University Press , Princeton N.J ., 198 . Zbl 0682.43001 · Zbl 0682.43001 [13] L. Boutet De Monvel and V. Guillemin , The Spectral Theory of Toeplitz Operators , Annals of Mathematics Studies 99 , Princeton University Press , Princeton N.J ., 1981 . MR 620794 | Zbl 0469.47021 · Zbl 0469.47021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.