A Charged Particle in an Electric Field in the Probability Representation of Quantum Mechanics

The Green's function and linear integrals of motion for a charged particle moving in an electric field are discussed. The Wigner functions and tomograms of the stationary states of the charged particle are obtained. The relationship between the quantum propagators for the Schrödinger evolution equation, the Moyal evolution equation, and the evolution equation in the tomographic-probability representation for a charged particle moving in an electric field is discussed.

[1]  C. Brif,et al.  Phase space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie group symmetries , 1998, quant-ph/9809052.

[2]  Vogel,et al.  Nonlinear coherent states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[3]  J. Bell,et al.  Speakable and Unspeakable in Quatum Mechanics , 1988 .

[4]  Olga V. Man'ko,et al.  Quantum states in probability representation and tomography , 1997 .

[5]  Vogel,et al.  Unbalanced homodyning for quantum state measurements. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[6]  Weigert.  Quantum time evolution in terms of nonredundant probabilities , 2000, Physical review letters.

[7]  O. Man'ko.  Symplectic tomography of nonlinear coherent states of a trapped ion , 1996, 1903.00882.

[8]  Stefano Mancini,et al.  Density matrix from photon number tomography , 1996, quant-ph/9612004.

[9]  G. Agarwal.  STATE RECONSTRUCTION FOR A COLLECTION OF TWO-LEVEL SYSTEMS , 1998 .

[10]  Banaszek,et al.  Direct probing of quantum phase space by photon counting. , 1996, Physical review letters.

[11]  V. I. Man'ko,et al.  Reconstructing the density operator by using generalized field quadratures , 1996, quant-ph/9606034.

[12]  J. Gracia-Bond́ıa,et al.  The Moyal representation for spin , 1989 .

[13]  E. Sudarshan.  Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams , 1963 .

[14]  The Pauli equation for probability distributions , 2000, quant-ph/0005058.

[15]  J. Wheeler,et al.  Quantum theory and measurement , 1983 .

[16]  Different realizations of the tomographic principle in quantum state measurement , 1997, quant-ph/9709012.

[17]  DIFFRACTION IN TIME IN TERMS OF WIGNER DISTRIBUTIONS AND TOMOGRAPHIC PROBABILITIES , 1999, quant-ph/9902075.

[18]  King,et al.  Generation of nonclassical motional states of a trapped atom. , 1996, Physical review letters.

[19]  J. Neumann.  Mathematische grundlagen der Quantenmechanik , 1935 .

[20]  P. Bertrand,et al.  A tomographic approach to Wigner's function , 1987 .

[21]  Schleich,et al.  Endoscopy in the Paul Trap: Measurement of the Vibratory Quantum State of a Single Ion. , 1996, Physical review letters.

[22]  Beck,et al.  Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum. , 1993, Physical review letters.

[23]  V. I. Man'ko,et al.  Classical formulation of quantum mechanics , 1996 .

[24]  Leonhardt,et al.  Discrete Wigner function and quantum-state tomography. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[25]  Vogel,et al.  Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase. , 1989, Physical review. A, General physics.

[26]  Samuel L Braunstein,et al.  Multi-dimensional Hermite polynomials in quantum optics , 2001 .

[27]  Stefano Mancini,et al.  Wigner function and probability distribution for shifted and squeezed quadratures , 1995 .

[28]  Properties of squeezed-state excitations , 1996, quant-ph/9612008.

[29]  Vladimir I. Man’ko,et al.  Positive distribution description for spin states , 1997 .

[30]  Classical-like description of quantum dynamics by means of symplectic tomography , 1996, quant-ph/9609026.