Quantum Mechanics By Amit Goswami Second Edition (informative)
Free download Quantum Mechanics By Amit Goswami Second Edition
2nd Edition
Authors of: Quantum Mechanics By Amit Goswami Second Edition
Amit Goswami
Table of Contents in Quantum Mechanics By Amit Goswami Second Edition
1. An Introduction to the Schrödinger Equation
2. The Motion of Wave Packets
3. Schrödinger Equation as Eigenvalue-Eigenfunction Equation
4. The Solution of the Schrödinger Equation in One Dimension
5. Looking through the Heisenberg-Bohr Microscope
6. The Dirac Description of Quantum Mechanical States
7. The One-Dimensional Harmonic Oscillator
8. Equations of Motion and Classical Correspondence
9. Systems of Two Degrees of Freedom
10. Quantum Paradoxes and the Copenhagen Interpretation
11. Angular Momentum
12. Motion in Central Potential
13. The Hydrogen Atom
14. Electrons in the Electromagnetic Field
15. Spin and Matrices
16. Matrix Mechanics: Two-State Systems
17. The Addition of Angular Momenta
18. Approximation Methods for Stationary States
19. Quantum Systems: Atoms with One and Two Electrons
20. Quantum Systems: Atoms and Molecules
21. Quantum Systems: Fermi and Bose Gases
22. Time-Dependent Perturbation Theory and Application to Atomic Radiation and Scattering
23. Scattering Theory
24. The Unfinished Chapter: The Meaning and Interpretation of Quantum Mechanics
Appendix. The Delta Function
1. An Introduction to the Schrödinger Equation
This chapter provides a fundamental introduction to the Schrödinger equation, a cornerstone of quantum mechanics. It discusses the origins, meaning, and significance of this wave equation in describing the behavior of quantum particles. It serves as the starting point for understanding quantum states and how they evolve over time.
2. The Motion of Wave Packets
This section focuses on the dynamics of wave packets, which describe the probabilistic motion of quantum particles. The concept of superposition and the spreading of wave packets are explored, along with the role they play in linking quantum and classical descriptions of motion.
3. Schrödinger Equation as Eigenvalue-Eigenfunction Equation
Here, the Schrödinger equation is introduced in its form as an eigenvalue-eigenfunction problem. The chapter explains how solving the equation yields allowed energy levels (eigenvalues) and associated wavefunctions (eigenfunctions) that describe the quantum states of a system.
4. The Solution of the Schrödinger Equation in One Dimension
This chapter examines the Schrödinger equation in the context of one-dimensional systems. Specific cases, such as the infinite potential well and the potential barrier, are discussed, providing insights into bound states, quantization of energy, and tunneling effects.
5. Looking through the Heisenberg-Bohr Microscope
This section discusses the thought experiment involving the Heisenberg-Bohr microscope, which illustrates the uncertainty principle. It emphasizes the fundamental limits of measurement in quantum mechanics and provides a conceptual framework for understanding the limitations of classical ideas in a quantum world.
6. The Dirac Description of Quantum Mechanical States
In this chapter, the Dirac formalism of quantum mechanics is introduced, offering an alternative but equivalent approach to the Schrödinger picture. The use of bras, kets, and operators in describing quantum states and observables is covered, laying the groundwork for understanding quantum mechanics in a more abstract and general form.
7. The One-Dimensional Harmonic Oscillator
This section explores the quantum mechanical treatment of the one-dimensional harmonic oscillator, a fundamental model in physics. The chapter discusses the quantization of energy levels and introduces ladder operators, providing insight into more complex quantum systems.
8. Equations of Motion and Classical Correspondence
The correspondence between quantum mechanics and classical physics is examined in this chapter. The equations of motion are explored in the context of classical and quantum descriptions, showing how classical mechanics emerges as a limit of quantum mechanics for large quantum numbers.
9. Systems of Two Degrees of Freedom
This section extends the study of quantum systems to those involving two degrees of freedom. Topics include coupled oscillators, particle interactions, and the role of entanglement, highlighting how these systems behave in the quantum realm.
10. Quantum Paradoxes and the Copenhagen Interpretation
This chapter delves into some of the famous paradoxes of quantum mechanics, such as Schrödinger’s cat and the measurement problem. The Copenhagen interpretation is discussed as a resolution to these paradoxes, emphasizing the probabilistic nature of quantum mechanics and the role of observation.
11. Angular Momentum
Here, the quantum mechanical treatment of angular momentum is explored. The chapter introduces the concept of quantized angular momentum and discusses how angular momentum operators are used to describe rotational motion in quantum systems.
12. Motion in Central Potential
This section examines the motion of particles in a central potential, such as the gravitational or electrostatic potential. The chapter provides solutions to the Schrödinger equation for such systems, emphasizing their application to spherically symmetric problems.
13. The Hydrogen Atom
A detailed study of the hydrogen atom, one of the most important quantum systems, is presented in this chapter. The solution to the Schrödinger equation for the hydrogen atom is discussed, along with the resulting quantized energy levels and the structure of the atom.
14. Electrons in the Electromagnetic Field
This chapter focuses on the behavior of electrons in an electromagnetic field. The interaction of charged particles with electric and magnetic fields is explored, including the quantum mechanical treatment of phenomena like the Aharonov-Bohm effect.
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