**Contemporary Mathematics**

Volume: 529;
2010;
202 pp;
Softcover

MSC: Primary 15; 47; 81; 82; 94;

Print ISBN: 978-0-8218-5247-7

Product Code: CONM/529

List Price: $73.00

Individual Member Price: $58.40

**Electronic ISBN: 978-0-8218-8208-5
Product Code: CONM/529.E**

List Price: $73.00

Individual Member Price: $58.40

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# Entropy and the Quantum

Share this page *Edited by *
*Robert Sims; Daniel Ueltschi*

These lecture notes provide a pedagogical introduction to quantum mechanics and to some of the mathematics that has been motivated by this field. They are a product of the school “Entropy and the Quantum”, which took place in Tucson, Arizona, in 2009. They have been written primarily for young mathematicians, but they will also prove useful to more experienced analysts and mathematical physicists. In the first contribution, William Faris introduces the mathematics of quantum mechanics. Robert Seiringer and Eric Carlen review certain recent developments in stability of matter and analytic inequalities, respectively. Bruno Nachtergaele and Robert Sims review locality results for quantum systems, and Christopher King deals with additivity conjectures and quantum information theory. The final article, by Christian Hainzl, describes applications of analysis to the Shandrasekhar limit of stellar masses.

#### Table of Contents

# Table of Contents

## Entropy and the Quantum

- Contents v6 free
- Preface vii8 free
- List of Participants ix10 free
- Outline of Quantum Mechanics 112 free
- 1. The setting for quantum mechanics 213
- 2. The Schrödinger equation 819
- 2.1. Diffusion and the free motion Schrödinger equation 819
- 2.2. The free particle 920
- 2.3. Shift operators 1223
- 2.4. The Schrödinger equation with a potential energy function 1223
- 2.5. Motion with constant force 1324
- 2.6. Spectral and propagator solutions 1425
- 2.7. Particle in a box 1526
- 2.8. Particle on the half-line 1728
- 2.9. The diffusion with drift representation 1829
- 2.10. The harmonic oscillator 1930

- 3. Self-adjoint operators 2334
- 4. The role of Planck's constant 3546
- 5. Spin and statistics 3849
- 6. Fundamental structures of quantum mechanics 4253
- Acknowledgments 5263
- References 5263

- Inequalities for Schrödinger Operators and Applications to the Stability of Matter Problem 5364
- Trace Inequalities and Quantum Entropy: An Introductory Course 7384
- 1. Introduction 7485
- 2. Operator convexity and monotonicity 8192
- 3. The joint convexity of certain operator functions 90101
- 4. Projections onto *-subalgebras and convexity inequalities 94105
- 5. Tensor products 108119
- 6. Lieb's Concavity Theorem and related results 118129
- 7. Lp norms for matrices and entropy inequalities 123134
- 8. Brascamp-Lieb type inequalities for traces 131142
- Acknoledgements 138149
- References 138149

- Lieb-Robinson Bounds in Quantum Many-Body Physics 141152
- Remarks on the Additivity Conjectures for Quantum Channels 177188
- On the Static and Dynamical Collapse of White Dwarfs 189200

#### Readership

Graduate students and research mathematicians interested in mathematical aspects of quantum physics.