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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 47, 1982 - Issue 5
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Original Articles

Wigner's phase space function and atomic structure

I. The hydrogen atom ground state

Jens Peder Dahl Department of Chemical Physics, Technical University of Denmark, DTH 301, DK-2800, Lyngby, Denmark
&
Michael Springborg Department of Chemical Physics, Technical University of Denmark, DTH 301, DK-2800, Lyngby, Denmark
Pages 1001-1019 | Received 25 May 1982, Accepted 29 Jun 1982, Published online: 22 Aug 2006

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J. P. Dahl, S. Varro, A. Wolf & W. P. Schleich. (2007) Weyl–Wigner correspondence in two space dimensions. Journal of Modern Optics 54:13-15, pages 2017-2032.
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Articles from other publishers (74)

Bálint Koczor, Frederik vom Ende, Maurice de Gosson, Steffen J. Glaser & Robert Zeier. (2023) Phase Spaces, Parity Operators, and the Born–Jordan Distribution. Annales Henri Poincaré 24:12, pages 4169-4236.
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Julien Toulouse. (2023) Semiclassical approximations of photoabsorption cross sections beyond the continuum threshold. The European Physical Journal A 59:5.
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Michael Kordell II, Rainer J. Fries & Che Ming Ko. (2022) Angular momentum eigenstates of the isotropic 3-D harmonic oscillator: Phase-space distributions and coalescence probabilities. Annals of Physics 443, pages 168960.
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Hongfei Zhan, Zhenning Cai & Guanghui Hu. (2022) The Wigner function of ground state and one-dimensional numerics. Journal of Computational Physics 449, pages 110780.
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A. X. Martins, R. A. S. Paiva, G. Petronilo, R. R. Luz, R. G. G. Amorim, S. C. Ulhoa & T. M. R. Filho. (2020) Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function. Advances in High Energy Physics 2020, pages 1-6.
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Chol Jong, Byong-Il Ri, Gwang-Dong Yu, Song-Guk Kim, Son-Il Jo & Shin-Hyok Jon. (2019) Ensemble in phase space: Statistical formalism of quantum mechanics. Pramana 92:5.
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Maurice de Gosson. (2018) Short-Time Propagators and the Born–Jordan Quantization Rule. Entropy 20:11, pages 869.
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P. Campos, M.G.R. Martins, M.C.B. Fernandes & J.D.M. Vianna. (2018) Quantum mechanics on phase space: The hydrogen atom and its Wigner functions. Annals of Physics 390, pages 60-70.
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P. Campos, M.G.R. Martins & J.D.M. Vianna. (2017) Quantum mechanics on phase space and the Coulomb potential. Physics Letters A 381:13, pages 1129-1133.
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Maurice A. de Gosson. (2016) The Angular Momentum Dilemma and Born–Jordan Quantization. Foundations of Physics 47:1, pages 61-70.
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Fateme Hoseini, Jayanta K. Saha & Hassan Hassanabadi. (2016) Investigation of Fermions in Non-commutative Space by Considering Kratzer Potential. Communications in Theoretical Physics 65:6, pages 695-700.
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Maurice A. de Gosson. (2016) From Weyl to Born–Jordan quantization: The Schrödinger representation revisited. Physics Reports 623, pages 1-58.
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Maurice A. de GossonMaurice A. de Gosson. 2016. Born-Jordan Quantization. Born-Jordan Quantization 147 159 .
J.M. Sellier & I. Dimov. (2014) The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations. Journal of Computational Physics 273, pages 589-597.
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J.M. Sellier & I. Dimov. (2014) A Wigner Monte Carlo approach to density functional theory. Journal of Computational Physics 270, pages 265-277.
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Philippe Blanchard, José M. Gracia-Bondiacutea & Joseph C. Várilly. (2012) Density functional theory on phase space. International Journal of Quantum Chemistry 112:4, pages 1134-1164.
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Leon Cohen. (2011) Local Virial and Tensor Theorems. The Journal of Physical Chemistry A 115:45, pages 12919-12923.
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Debajit Chakraborty & Paul W. Ayers. 2011. Statistical Complexity. Statistical Complexity 35 48 .
W.P. Schleich, J.P. Dahl & S. Varró. (2010) Wigner function for a free particle in two dimensions: A tale of interference. Optics Communications 283:5, pages 786-789.
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A. V. Luzanov. (2008) Spectral and entropic characterizations of Wigner functions: Applications to model vibrational systems. The Journal of Chemical Physics 129:9.
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J. P. Dahl, S. Varro, A. Wolf & W. P. Schleich. (2007) Wigner functions of waves . Physical Review A 75:5.
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Ludmiła Praxmeyer, Jan Mostowski & Krzysztof Wódkiewicz. (2006) Hydrogen atom in phase space: the Wigner representation. Journal of Physics A: Mathematical and General 39:45, pages 14143-14151.
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Hartmut Schmider. (2006) Wigner Functions and Bond Orders. Zeitschrift für Physikalische Chemie 220:7_2006, pages 859-884.
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J Stanek & J Konarski. (2006) Wigner function for the radial equation of the Coulomb problem in Langer space. Journal of Physics A: Mathematical and General 39:1, pages 209-217.
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Peter M. W. Gill, Deborah L. Crittenden, Darragh P. O’Neill & Nicholas A. Besley. (2006) A family of intracules, a conjecture and the electron correlation problem. Phys. Chem. Chem. Phys. 8:1, pages 15-25.
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M. Belloni, M. A. Doncheski & R. W. Robinett. (2004) Wigner quasi-probability distribution for the infinite square well: Energy eigenstates and time-dependent wave packets. American Journal of Physics 72:9, pages 1183-1192.
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Jens Peder Dahl. (2004) Atomic Wigner Functions. Acta Physica Hungarica B) Quantum Electronics 20:1-2, pages 143-147.
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Tobias Schneider & Jan-Michael Rost. (2003) Double photoionization of two-electron atoms based on the explicit separation of dominant ionization mechanisms. Physical Review A 67:6.
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L. Praxmeyer & K. Wódkiewicz. (2003) Hydrogen atom in phase space: The Kirkwood-Rihaczek representation. Physical Review A 67:5.
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Nicholas A. Besley, Darragh P. O’Neill & Peter M. W. Gill. (2003) Computation of molecular Hartree–Fock Wigner intracules. The Journal of Chemical Physics 118:5, pages 2033-2038.
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Jens Peder Dahl. 2003. Fundamental World of Quantum Chemistry. Fundamental World of Quantum Chemistry 237 260 .
Thomas L Curtright & Cosmas K Zachos. (2002) Deformation quantization of superintegrable systems and Nambu mechanics. New Journal of Physics 4, pages 83-83.
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Jens P. Dahl. 2002. 100 Years Werner Heisenberg. 100 Years Werner Heisenberg 201 206 .
COSMAS ZACHOS. (2012) DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE. International Journal of Modern Physics A 17:03, pages 297-316.
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Jens Peder Dahl & Wolfgang P. Schleich. (2002) Concepts of radial and angular kinetic energies. Physical Review A 65:2.
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John Avery. 2002. Hyperspherical Harmonics and Generalized Sturmians. Hyperspherical Harmonics and Generalized Sturmians 119 192 .
Jens Peder Dahl. 2001. New Perspectives in Quantum Systems in Chemistry and Physics, Part 1. New Perspectives in Quantum Systems in Chemistry and Physics, Part 1 1 18 .
Jens Peder Dahl & Michael Springborg. (1999) Comment on “Wigner phase-space distribution function for the hydrogen atom”. Physical Review A 59:5, pages 4099-4100.
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Jens Peder Dahl. (1998) On the Einstein–Stern model of rotational heat capacities. The Journal of Chemical Physics 109:24, pages 10688-10691.
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Hartmut Schmider. (1996) A parity function for studying the molecular electronic structure. The Journal of Chemical Physics 105:24, pages 11134-11142.
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Hartmut Schmider & Jens Peder Dahl. (1996) Nodal structure of the electronic Wigner function of many-electron atoms and molecules. International Journal of Quantum Chemistry 60:1, pages 439-452.
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Hartmut Schmider. (1996) ‘‘Low-momentum electrons’’ and the electronic structure of small molecules. The Journal of Chemical Physics 105:9, pages 3627-3635.
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Hartmut Schmider & Minhhuy Hô. (1996) Molecular Networks in Position, Momentum, and Phase Space:  A Case Study on Simple Hydrocarbons. The Journal of Physical Chemistry 100:45, pages 17807-17819.
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M. Gadella. (1995) Moyal Formulation of Quantum Mechanics. Fortschritte der Physik/Progress of Physics 43:3, pages 229-264.
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John E. Harriman & Mark E. Casida. (2004) Husimi representation for stationary states. International Journal of Quantum Chemistry 45:3, pages 263-294.
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Jens Peder Dahl & Bjarne Amstrup. (1992) On kinetic energy densities. Journal of Molecular Structure: THEOCHEM 261, pages 345-353.
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John E. Harriman. (1992) Chemical bonds and momentum anisotropy in phase space. Journal of Molecular Structure: THEOCHEM 259, pages 141-154.
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Swapan K. Ghosh & Asish K. Dhara. (1991) Operator equation of motion in phase space: Application to time-dependent systems possessing invariants. Physical Review A 44:1, pages 65-71.
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Robert C. Morrison & Robert G. Parr. (2004) Approximate density matrices and Husimi functions using the maximum entropy formulation with constraints. International Journal of Quantum Chemistry 39:6, pages 823-837.
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Robert C. Morrison, Weitao Yang, Robert G. Parr & Chengteh Lee. (1990) Approximate density matrices and wigner distribution functions from density, kinetic energy density, and idempotency constraints. International Journal of Quantum Chemistry 38:6, pages 819-830.
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G R Shin & J Rafelski. (1990) Muons after d-t fusion. Journal of Physics G: Nuclear and Particle Physics 16:9, pages L187-L195.
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A Schmidt, M Horbatsch & R M Dreizler. (1990) Semiclassical phase space description of ionisation and capture for ions colliding with hydrogen-like targets. Journal of Physics B: Atomic, Molecular and Optical Physics 23:13, pages 2327S-2340S.
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John E. Harriman. (1990) N-representability of phase space functions for electrons. International Journal of Quantum Chemistry 38:S24, pages 119-128.
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James L. Anchell & John E. Harriman. (1990) Local electron momentum anisotropy in molecules. The Journal of Chemical Physics 92:5, pages 2943-2952.
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Joseph C. V�rilly, Jos� M. Gracia-Bond�a & Walter Schempp. (1990) The Moyal representation of quantum mechanics and special function theory. Acta Applicandae Mathematicae 18:3, pages 225-250.
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M Gadella, J M Gracia-Bondia, L M Nieto & J C Varilly. (1989) Quadratic Hamiltonians in phase-space quantum mechanics. Journal of Physics A: Mathematical and General 22:14, pages 2709-2738.
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Joachim J. Włodarz. (1988) A note on the wigner distribution function. Physics Letters A 133:9, pages 459-460.
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Lipo Wang & R. F. O'Connell. (1988) Quantum mechanics without wave functions. Foundations of Physics 18:10, pages 1023-1033.
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A.C. Tanner. (1988) The bond directional principle for momentum space wavefunctions: comments and cautions. Chemical Physics 123:2, pages 241-247.
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Jens Peder Dahl & Michael Springborg. (1988) The Morse oscillator in position space, momentum space, and phase space. The Journal of Chemical Physics 88:7, pages 4535-4547.
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C. Lee & L. Cohen. (1988) Instantaneous mean qualities in time-frequency analysis. Instantaneous mean qualities in time-frequency analysis.
Swapan K. Ghosh. (1987) A unified approach to local force laws in quantum chemistry. The Journal of Chemical Physics 87:6, pages 3513-3517.
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Y. S. Kim & E. P. Wigner. (1987) Covariant phase-space representation for localized light waves. Physical Review A 36:3, pages 1293-1297.
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Michael Springborg & Jens Peder Dahl. (1987) Wigner’s phase-space function and atomic structure: II. Ground states for closed-shell atoms. Physical Review A 36:3, pages 1050-1062.
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John Avery. (1987) Correlation in iterated solutions of the momentum-space schrödinger equation. Chemical Physics Letters 138:6, pages 520-524.
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Swapan K Ghosh. (1987) Quantum chemistry in phase space: Some current trends. Journal of Chemical Sciences 99:1-2, pages 21-28.
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Mark E. Casida, John E. Harriman & James L. Anchell. (1987) The Husimi function for electron distributions. International Journal of Quantum Chemistry 32:S21, pages 435-456.
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Ajit J. Thakkar, Anthony C. Tanner & Vedene H. SmithJr.Jr.. 1987. Density Matrices and Density Functionals. Density Matrices and Density Functionals 327 337 .
J. P. Dahl. 1987. The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function. The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function 241 243 .
Jens Peder DAHL. 1985. Semiclassical Descriptions of Atomic and Nuclear Collisions. Semiclassical Descriptions of Atomic and Nuclear Collisions 379 394 .
Michael Springborg. (1984) On semiclassical approximations to Wigner's phase space function. Physica A: Statistical Mechanics and its Applications 126:1-2, pages 259-270.
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Michael Springborg & Jens Peder Dahl. 1984. Local Density Approximations in Quantum Chemistry and Solid State Physics. Local Density Approximations in Quantum Chemistry and Solid State Physics 381 412 .
John E. Harriman. (2009) Density matrix and density functional theory with a gaussian wavepacket basis. International Journal of Quantum Chemistry 24:S17, pages 501-515.
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Michael Springborg. (1983) Wigner's phase space function and the bond in LiH. Theoretica Chimica Acta 63:4, pages 349-356.
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