bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Barletti, Luigi:
A mathematical introduction to the Wigner formulation of quantum mechanics
Bollettino dell'Unione Matematica Italiana Serie 8 6-B (2003), fasc. n.3, p. 693-716, Unione Matematica Italiana (English)
pdf (320 Kb), djvu (321 Kb). | MR2014828 | Zbl 1117.81091

Sunto

Il presente articolo è una rassegna di alcuni aspetti matematici fondamentali della formulazione Wigneriana della meccanica quantistica. A partire dagli assiomi della meccanica quantistica e della meccanica statistica quantistica viene motivata l'introduzione della trasformazione di Wigner e viene infine dedotta l'equazione di Wigner.
Referenze Bibliografiche
[1] A. ARNOLD-H. LANGE-P. F. ZWEIFEL, A discrete-velocity stationary Wigner equation, J. Math. Phys., 41 (2000), 7167-7180. | MR 1788568 | Zbl 1019.82020
[2] A. ARNOLD-H. STEINRÜCK, The "electromagnetic" Wigner equation for an electron with spin, Z. Angew. Math. Phys., 40 (1989), 793-815. | MR 1027576 | Zbl 0701.35130
[3] J. BANASIAK-L. BARLETTI, On the existence of propagators in stationary Wigner equation without velocity cut-off, Transport Theory Stat. Phys., 30 (2001), 659-672. | MR 1865352 | Zbl 0990.82019
[4] L. BARLETTI-P. F. ZWEIFEL, Parity-decomposition method for the stationary Wigner equation with inflow boundary conditions, Transport Theory Stat. Phys., 30 (2001), 507-520. | MR 1866627 | Zbl 1006.82032
[5] N. BEN ABDALLAH-P. DEGOND-I. GAMBA, Inflow boundary conditions for the time dependent one-dimensional Schrödinger equation, C. R. Acad. Sci. Paris, Sér. I Math., 331 (2000), 1023-1028. | MR 1809447 | Zbl 1158.35344
[6] P. BILLINGSLEY, Probability and Measure (third edition), Wiley, 1995. | MR 1324786 | Zbl 0822.60002
[7] P. BORDONE-M. PASCOLI-R. BRUNETTI-A. BERTONI-C. JACOBONI, Quantum transport of electrons in open nanostructures with the Wigner-function formalism, Phys. Rev. B, 59 (1999), 3060-3069.
[8] P. CARRUTHERS-F. ZACHARIASEN, Quantum collision theory with phase-space distributions, Rev. Mod. Phys., 55 (1983), 245-285. | MR 698046
[9] T. A. CLAASEN-W. F. MECKLENBRÄUKER, The Wigner distribution - a tool for time-frequency signal analysis, Philips J. Res., 35 (1980), 217-250. | MR 590577 | Zbl 0474.94007
[10] S. R. DE GROOT-L. G. SUTTORP, Foundations of Electrodynamics, North-Holland, 1972.
[11] D. K. FERRY-S. M. GOODNICK, Transport in Nanostructures, Cambridge University Press, 1997.
[12] R. P. FEYNMAN, Statistical Mechanics, W. A. Benjamin Inc., 1972. | Zbl 0997.82500
[13] G. B. FOLLAND, Harmonic Analysis in Phase Space, Princeton University Press, 1989. | MR 983366 | Zbl 0682.43001
[14] W. R. FRENSLEY, Boundary conditions for open quantum systems driven far from equilibrium, Rev. Modern Phys., 62 (1990), 745-791.
[15] F. FROMMLET, Time irreversibility in quantum mechanical systems, PhD thesis, Technischen Universität Berlin, 2000.
[16] P. GÉRARD-P. A. MARKOWICH-N. J. MAUSER-F. POUPAUD, Homogenization limits and Wigner transforms, Comm. Pure Appl. Math., 50 (1997), 323-379. | MR 1438151 | Zbl 0881.35099
[17] R. L. LIBOFF, Kinetic Theory: Classical, Quantum and Relativistic Descriptions, Wiley, 1998.
[18] P. L. LIONS-T. PAUL, Sur les mesures de Wigner, Rev. Matematica Iberoamericana, 9 (1993), 553-618. | MR 1251718 | Zbl 0801.35117
[19] G. W. MACKEY, The Mathematical Foundations of Quantum Mechanics, W. A. Benjamin Inc., 1963. | Zbl 0114.44002
[20] P. A. MARKOWICH, On the equivalence of the Schrödinger and the quantum Liouville equations, Math. Meth. Appl. Sci., 11 (1989), 459-469. | MR 1001097 | Zbl 0696.47042
[21] P. A. MARKOWICH-N. J. MAUSER-F. POUPAUD, A Wigner function approach to (semi)classical limits: Electrons in a periodic potential, J. Math. Phys., 35 (1994), 1066-1094. | MR 1262733 | Zbl 0805.35106
[22] P. A. MARKOWICH-C. A. RINGHOFER-C. SCHMEISER, Semiconductor Equations, Springer Verlag, 1990. | MR 1063852 | Zbl 0765.35001
[23] J. VON NEUMANN, Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955. | MR 66944 | Zbl 0064.21503
[24] M. REED-B. SIMON, Methods of Modern Mathematical Physics, I - Functional Analysis, Academic Press, 1972. | MR 493419 | Zbl 0242.46001
[25] V. I. TATARSKIĬ, The Wigner representation of quantum mechanics, Sov. Phys. Usp., 26 (1983), 311-327. | MR 730012
[26] H. WEYL, The Theory of Groups and Quantum Mechanics, Dover, 1950. | Zbl 0041.56804 | Jbk 58.1374.01
[27] E. WIGNER, On the quantum correction for thermodynamic equilibrium, Phys. Rev., 40 (1932), 749-759. | Jbk 58.0948.07
[28] P. ZHAO-H. L. CUI-D. L. WOOLARD-K. L. JENSEN-F. A. BUOT, Equivalent circuit parameters of resonant tunneling diodes extracted from self-consistent Wigner-Poisson simulation, IEEE Transactions on Electron Devices, 48 (2001), 614-626.

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali