Non-Relativistic Quantum Mechanics

Quantum mechanics, from its birth to quantum information, is explained in a simple way using established mathematical techniques.

Ravinder R. Puri (Author)

9781107164369, Cambridge University Press

Hardback, published 4 July 2017

452 pages
24.8 x 18.3 x 2.6 cm, 0.88 kg

This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail.

Preface
1. History of quantum mechanics
2. Vectors and operators
3. Finite dimensional spaces
4. Function space
5. Postulates of quantum mechanics
6. Density operator
7. Measurement postulate and paradoxes of quantum mechanics
8. Position and momentum representations
9. Schrödinger equation in one dimension
10. One-dimensional piecewise constant potentials
11. One-dimensional exactly solvable continuous potentials
12. Partially and completely periodic potentials
13. Harmonic oscillator
14. Three-dimensional central potentials
15. Symmetry in quantum mechanics
16. Quantum theory of angular momentum
17. Approximation methods
18. Entanglement and local hidden variable theory
Appendix A. Delta function
Appendix B. Second-order ordinary differential equations
Appendix C. Riccati equation
Appendix D. Some mathematical formulas
References
Index.

Subject Areas: Chemical physics [PHVQ], Quantum physics [quantum mechanics & quantum field theory PHQ], Atomic & molecular physics [PHM]