Non-Relativistic Quantum Mechanics
About this book
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.
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Information
Table of contents
- Cover
- Non-Relativistic Quantum Mechanics
- Title
- Copyright
- Dedication
- Contents
- Preface
- CHAPTER 1: History of Quantum Mechanics
- CHAPTER 2: Vectors and Operators
- CHAPTER 3: Finite Dimensional Spaces
- CHAPTER 4: Function Space
- CHAPTER 5: Postulates of Quantum Mechanics
- CHAPTER 6: Density Operator
- CHAPTER 7: Measurement Postulate and Paradoxes of Quantum Mechanics
- CHAPTER 8: Position and Momentum Representations
- CHAPTER 9: Schrödinger Equation in One Dimension
- CHAPTER 10: One-Dimensional Piecewise Constant Potentials
- CHAPTER 11: One-Dimensional Exactly Solvable Continuous Potentials
- CHAPTER 12: Partially and Completely Periodic Potentials
- CHAPTER 13: Harmonic Oscillator
- CHAPTER 14: Three-Dimensional Central Potentials
- CHAPTER 15: Symmetry in Quantum Mechanics
- CHAPTER 16: Quantum Theory of Angular Momentum
- CHAPTER 17: Approximation Methods
- CHAPTER 18: Entanglement and Local Hidden Variable Theory
- Appendices
- References
- Bibliography
- Index
