 | Advances in quantum chemistry. Vol.57, Part 1: Theory of confined quantum systems / ed. by J.S.Sabin, E.Brändas; spec. editor S.A.Cruz. - Oxford: Elsevier/Academic Press, 2009. - xii, 334 p.: ill. - Incl. bibl. ref. - Sub. ind.: p.319-334. - ISBN 978-0-12-374764-8
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1 Properties of Confined Hydrogen and Helium Atoms
S.H. Patil and Y.P. Varshni .................................. 1
1 Introduction .............................................. 1
2 Some General Properties ................................... 2
3 H in a Spherical Box ...................................... 5
4 H in Confining Oscillator Potential ...................... 19
5 Off-centre Confinement ................................... 21
6 Summary .................................................. 23
References .................................................. 24
2 Exact Relations for Confined One-Electron Systems
K.D. Sen, V.I. Pupyshev and H.E. Montgomery Jr. ............. 25
1 Introduction: Some Notes on History ...................... 26
2 Some General Constructions and Notations ................. 28
3 Commutation Relations and Hypervirial Theorems ........... 33
4 Energy and Region Modifications .......................... 40
5 The System in an External Potential ...................... 51
6 On Mean Values and Other Properties of Confined Systems .. 58
7 Spherically Confined Isotropic Harmonic Oscillator ....... 68
8 Information Theoretical Uncertainty-like Relationships ... 69
9 Afterword ................................................ 71
Acknowledgments ............................................. 72
References .................................................. 72
3 The Hydrogen Atom Confined in Semi-infinite Spaces Limited
by Conoidal Boundaries
Eugenio Ley-Koo ............................................. 79
1 Introduction ............................................. 80
2 Sample of Comments on Articles About Confined Atoms and
Molecules ................................................ 82
3 Review of The Superintegrability of The Schrцdinger
Equation for The Free Hydrogen Atom and its Ionization
Limit .................................................... 90
4 Overview of the Confinement of the Hydrogen Atom by
a Conoidal Boundary as a Symmetry-Breaking Effect ....... 103
5 Preview of Problems on Confined Atoms and Molecules of
Current and Future Investigations ....................... 113
6 Discussion .............................................. 119
Acknowledgements ........................................... 120
References ................................................. 121
4 The Hydrogen and Helium Atoms Confined in Spherical Boxes
N. Aquino .................................................. 123
1 Introduction ............................................ 123
2 Methods used in Various Studies of the Confined
Hydrogen Atom ........................................... 125
3 Soft Spherical Confinement for Hydrogen Atom
Revisited ............................................... 148
4 Treatment of the Confined Hydrogen Atom Under Neumann
Boundary Conditions ..................................... 151
5 The Helium Atom Confined in Spherical Boxes ............. 152
6 Other Approaches ........................................ 164
7 Conclusions ............................................. 166
Acknowledgments ............................................ 167
References ................................................. 167
5 Exact Solutions for Confined Model Systems Using Kummer
Functions
B.L. Burrows and M. Cohen .................................. 173
1 Introduction ............................................ 173
2 Solutions of Kummer's Equation .......................... 176
3 K-dimensional Systems ................................... 184
4 Confined Hydrogen Atom in 3-d and 2-d ................... 190
5 Two-dimensional Harmonic Oscillator ..................... 196
6 The Constant Potential .................................. 196
7 Summary ................................................. 198
Acknowledgements ........................................... 199
Appendix ................................................... 199
References ................................................. 201
6 Perturbation Theory for a Hydrogen-like Atom Confined
Within an Impenetrable Spherical Cavity
Cecil Laughlin ............................................. 203
1 Introduction ............................................ 203
2 Asymptotic Expansions for Large Box Radii ............... 205
3 Expansions for Smalt Box Radii .......................... 214
4 Variational and Numerical Solutions ..................... 220
5 Perturbation Theory Results for Small Box Radii ......... 222
6 Intermediate Box Sizes .................................. 232
7 Concluding Remarks ...................................... 236
References ................................................. 238
7 Comparative Study Between the Hartree-Fock and Kohn-Sham
Models for the Lowest Singlet and Triplet States of the
Confined Helium Atom
Jorge Garza and Rubicelia Vargas ........................... 241
1 Introduction ............................................ 241
2 Hartree-Fock and Kohn-Sham Models for Two-electron
Systems ................................................. 242
3 Methodology ............................................. 246
4 Results and Discussion .................................. 246
5 Conclusions ............................................. 253
Acknowledgments ............................................ 254
References ................................................. 254
8 Thomas-Fermi-Dirac-Weizsдcker Density Functional
Formalism Applied to the Study of Many-electron Atom
Confinement by Open and Closed Boundaries
Salvador A. Cruz ........................................... 255
1 Introduction ............................................ 255
2 Many-electron Atom Confinement by Closed Boundaries ..... 257
3 Many-electron Atom Confinement by Open Boundaries ....... 275
4 Conclusions ............................................. 281
References ................................................. 282
9 Confined Atoms Treated as Open Quantum Systems
Richard F.W. Bader ......................................... 285
1 Physically Confined Systems are Open Systems ............ 285
2 Mechanics of an Open System ............................. 286
3 Virial Theorem and the Definition of Pressure ........... 289
4 Calculation of Pressure in Terms of the Surface Virial .. 293
5 Discussion and Conclusions .............................. 316
Acknowledgements ........................................... 317
References ................................................. 317
Index ......................................................... 319
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