Ebook: Solvable Models in Quantum Mechanics

Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.

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Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-8
Front Matter....Pages 9-9
The One-Center Point Interaction in Three Dimensions....Pages 11-51
Coulomb Plus One-Center Point Interaction in Three Dimensions....Pages 52-74
The One-Center ?-Interaction in One Dimension....Pages 75-90
The One-Center ?’-Interaction in One Dimension....Pages 91-96
The One-Center Point Interaction in Two Dimensions....Pages 97-105
Front Matter....Pages 107-107
Finitely Many Point Interactions in Three Dimensions....Pages 109-139
Finitely Many ?-Interactions in One Dimension....Pages 140-153
Finitely Many ?’-Interactions in One Dimension....Pages 154-159
Finitely Many Point Interactions in Two Dimensions....Pages 160-166
Front Matter....Pages 167-167
Infinitely Many Point Interactions in Three Dimensions....Pages 169-252
Infinitely Many ?-Interactions in One Dimension....Pages 253-306
Infinitely Many ?’-Interactions in One Dimension....Pages 307-323
Infinitely Many Point Interactions in Two Dimensions....Pages 324-333
Random Hamiltonians with Point Interactions....Pages 334-354
Back Matter....Pages 355-452

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Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-8
Front Matter....Pages 9-9
The One-Center Point Interaction in Three Dimensions....Pages 11-51
Coulomb Plus One-Center Point Interaction in Three Dimensions....Pages 52-74
The One-Center ?-Interaction in One Dimension....Pages 75-90
The One-Center ?’-Interaction in One Dimension....Pages 91-96
The One-Center Point Interaction in Two Dimensions....Pages 97-105
Front Matter....Pages 107-107
Finitely Many Point Interactions in Three Dimensions....Pages 109-139
Finitely Many ?-Interactions in One Dimension....Pages 140-153
Finitely Many ?’-Interactions in One Dimension....Pages 154-159
Finitely Many Point Interactions in Two Dimensions....Pages 160-166
Front Matter....Pages 167-167
Infinitely Many Point Interactions in Three Dimensions....Pages 169-252
Infinitely Many ?-Interactions in One Dimension....Pages 253-306
Infinitely Many ?’-Interactions in One Dimension....Pages 307-323
Infinitely Many Point Interactions in Two Dimensions....Pages 324-333
Random Hamiltonians with Point Interactions....Pages 334-354
Back Matter....Pages 355-452
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