A Course in Quantum Mechanics.

Cover -- Title Page -- Copyright Page -- Dedication -- Preface -- Contents -- Notations &amp -- Fundamental Constants -- 1 Basic Concepts &amp -- Formulation -- 1.1 Introduction -- 1.2 Measurements -- 1.3 Basic Postulates -- (i) Postulate 1. State of the System -- (ii) Postulate 2. Superposition of States -- (iii) Postulate 3. Operators for Dynamical Variables -- (iv) Postulate 4. Eigenvalues and Eigenvectors of Operators -- (v) Postulate 5. Hermitian Operator -- (vi) Postulate 6. Basis Vectors and Completeness Condition -- (vii) Expectation Value -- 2 Representation Theory -- 2.1 Elements of Representation Theory -- (i) The Energy Representation, called the E-representatrion -- (ii) Operators as Matrices -- 2.2 Change in Representation and Unitary Transformation -- 2.3 Commuting Observables -- 2.4 Uncertainty Relation -- 3 Position &amp -- Momentum Operators -- 3.1 Position Operator and its Eigenkets -- 3.2 Spatial Translation and Momentum Operator -- 3.3 Momentum Operator in Position Basis -- 3.4 Momentum Wavefunction -- 3.5 Gaussian as Minimum Uncertainty Wave Packet -- 3.6 Extension to Three Dimension -- 4 Time Evolution of Quantum Systems -- 4.1 Time Evolution Operator -- 4.2 The Schrödinger Equation of Motion -- 4.3 Time Dependence of Expectation Values: Ehrenfest Theorem -- 4.4 The Schrödinger and Heisenberg Pictures -- 4.5 The Heisenberg Equation of Motion -- 4.6 Operator Form of the Hamiltonian: Classical Analogue -- 4.7 Time Dependence of the Base Kets -- 5 Propagators and Feynman Path Integral -- 5.1 Propagators -- 5.2 Feynman's Path -- 6 Application in One Dimension -- 6.1 Free Particle -- 6.2 Rectangular Potential Well -- (i) Bound State Solution -- (ii) Unbound State Solution -- 6.3 Rectangular Potential Barrier -- 6.4 Delta Function Potential -- 6.5 Oscillator Problem by Schrödinger Method.

6.6 Linear Harmonic Oscillator by Operator Method -- (i) Time Evolution of Oscillator -- (ii) Coherent State -- 6.7 Periodic Potential -- 7 Rotation and Angular Momentum -- 7.1 Introduction -- 7.2 Rotation in Three Dimension -- 7.3 Rotation of System Kets -- 7.4 Eigenvalue and Eigenvectors of Angular Momentum -- 7.5 Matrix Representation of Angular Momentum Operator -- 7.6 Orbital Angular Momentum -- 8 Spin Angular Momentum -- 8.1 The Stern Gerlach Experiment -- 8.2 Matrix Representation of Spin -- 8.3 Finite Rotations in Spin-½ Space -- 8.4 Pauli Two Component Spinor Formalism -- 9 Addition of Angular Momenta -- 9.1 Addition of Two Angular Momenta Ĵ[sub(1)] and Ĵ[sub(2)] -- 9.2 Addition of Orbital Angular Momentum and Spin of a Particle -- 9.3 Addition of Two Spins -- 10 Applications II -- 10.1 Hydrogen Atom -- 10.2 Charged Particle in Magnetic Field -- (i) The Landau Levels -- (ii) The Aharanov Bohm Effect -- 11 Symmetry in Quantum Mechanics -- 11.1 Symmetry Principle and Conservation Laws -- (i) Symmetry and Degeneracy -- 11.2 Space Reflection or Parity Operation -- 11.3 Time Reversal Symmetry -- 12 Approximate Methods -- 12.1 Semiclassical Aprroximation or WKB Method -- 12.2 Rayleigh Schrödinger Perturbation -- (i) Non-Degenerate Case -- (ii) Perturbation Calculations for Degenerate Energy Levels -- 12.3 The Variational Method -- 13 Methods for Time Dependent Problems -- 13.1 Time Dependent Perturbation -- 13.2 Harmonic Perturbation -- (i) Fermi's Golden Rule -- (ii) Ionization of Hydrogen Atom -- 13.3 Adiabatic Approximation -- 13.4 The Sudden Approximation -- 14 Scattering Theory I -- 14.1 Scattering Experiments: Cross Section -- 14.2 Potential Scattering -- 14.3 The Method of Partial Waves -- 14.4 The Optical Theorem -- 15 Scattering Theory II -- 15.1 The Lippmann Schwinger Equation -- 15.2 The Born Approximation.

15.3 The Higher Order Born Approximation -- 16 Relativistic Wave Equations -- 16.1 Introduction -- 16.2 The Klein Gordon Equation -- 16.3 The Dirac Relativistic Equation -- 16.4 Conclusion -- A: Appendix -- A.1 Expansion in a Series of Orthonormal Functions -- A.2 Fourier Series -- A.3 Fourier Transforms -- A.4 The Dirac Delta Function -- Bibliography -- Index.

The book includes modern topics like coherent states, propagators and Feynman's path integral method, Landau levels, Aharonov Bohm Effect, parity operation, time reversal symmetry and Dirac relativisticequation. Please note: Taylor & Francis does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.