Description
CAMBRIDGE INDIA Non Relativistic Quantum Mechanics 2017 Edition by RAVINDER R. PURI
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.Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postulatesCovers advance topics such as the foundations of quantum mechanics, quantum information theory and nano-science in detailDiscusses density operator in general, and that of one- and two-level systemsOne-dimensional potentials for which the Schrödinger equation is exactly solvable are identified and explained comprehensivelyA general theory of one-dimensional partially and completely periodic potentials for the study of nano and bulk solids is developedTable of ContentsPreface1. History of quantum mechanics2. Vectors and operators3. Finite dimensional spaces4. Function space5. Postulates of quantum mechanics6. Density operator7. Measurement postulate and paradoxes of quantum mechanics8. Position and momentum representations9. Schrödinger equation in one dimension10. One-dimensional piecewise constant potentials11. One-dimensional exactly solvable continuous potentials12. Partially and completely periodic potentials13. Harmonic oscillator14. Three-dimensional central potentials15. Symmetry in quantum mechanics16. Quantum theory of angular momentum17. Approximation methods18. Entanglement and local hidden variable theoryAppendix A. Delta functionAppendix B. Second-order ordinary differential equationsAppendix C. Riccati equationAppendix D. Some mathematical formulasReferencesIndex.