Ebook: Quantum Mechanics: Theory and Applications

An understanding of quantum mechanics is vital to all students of physics, chemistry and electrical engineering, but requires a lot of mathematical concepts, the details of which are given with great clarity in this book. Various concepts have been derived from first principles, so it can also be used for self-study. The chapters on the JWKB approximation, time-independent perturbation theory and effects of magnetic field stand out for their clarity and easy-to-understand mathematics. Two complete chapters on the linear harmonic oscillator provide a very detailed discussion of one of the most fundamental problems in quantum mechanics. Operator algebra is used to show the ease with which one can calculate the harmonic oscillator wave functions and study the evolution of the coherent state. Similarly, three chapters on angular momentum give a detailed account of this important problem. Perhaps the most attractive feature of the book is the excellent balance between theory and applications and the large number of applications in such diverse areas as astrophysics, nuclear physics, atomic and molecular spectroscopy, solid-state physics, and quantum well structures.

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An understanding of quantum mechanics is vital to all students of physics, chemistry and electrical engineering, but requires a lot of mathematical concepts, the details of which are given with great clarity in this book. Various concepts have been derived from first principles, so it can also be used for self-study. The chapters on the JWKB approximation, time-independent perturbation theory and effects of magnetic field stand out for their clarity and easy-to-understand mathematics. Two complete chapters on the linear harmonic oscillator provide a very detailed discussion of one of the most fundamental problems in quantum mechanics. Operator algebra is used to show the ease with which one can calculate the harmonic oscillator wave functions and study the evolution of the coherent state. Similarly, three chapters on angular momentum give a detailed account of this important problem. Perhaps the most attractive feature of the book is the excellent balance between theory and applications and the large number of applications in such diverse areas as astrophysics, nuclear physics, atomic and molecular spectroscopy, solid-state physics, and quantum well structures.

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An understanding of quantum mechanics is vital to all students of physics, chemistry and electrical engineering, but requires a lot of mathematical concepts, the details of which are given with great clarity in this book. Various concepts have been derived from first principles, so it can also be used for self-study. The chapters on the JWKB approximation, time-independent perturbation theory and effects of magnetic field stand out for their clarity and easy-to-understand mathematics. Two complete chapters on the linear harmonic oscillator provide a very detailed discussion of one of the most fundamental problems in quantum mechanics. Operator algebra is used to show the ease with which one can calculate the harmonic oscillator wave functions and study the evolution of the coherent state. Similarly, three chapters on angular momentum give a detailed account of this important problem. Perhaps the most attractive feature of the book is the excellent balance between theory and applications and the large number of applications in such diverse areas as astrophysics, nuclear physics, atomic and molecular spectroscopy, solid-state physics, and quantum well structures.
Content:
Front Matter....Pages i-xlviii
Front Matter....Pages 1-1
The Dirac Delta Function....Pages 3-18
Fourier Transforms....Pages 19-27
Front Matter....Pages 29-29
Particles and Waves and the Uncertainty Principle....Pages 31-70
Time Dependent Schr?dinger Equation....Pages 71-88
Propagation of Wave Packets and Concept of Group Velocity....Pages 89-114
Bound State Solutions of the Schr?dinger Equation....Pages 115-158
Linear Harmonic Oscillator: I Solution of the Schr?dinger Equation and Relationship with the Classical Oscillator....Pages 159-196
One-Dimensional Barrier Transmission Problems....Pages 197-220
Angular Momentum I—The Spherical Harmonics....Pages 221-244
Spherically Symmetric Potentials Hydrogen Atom Problem, Rotation Vibration Spectra, Three-Dimensional Oscillator....Pages 245-290
Dirac’s Bra and Ket Algebra....Pages 291-307
Linear Harmonic Oscillator II Solutions Using Bra and Ket Algebra....Pages 308-338
Angular Momentum II Using Bra and Ket Algebra....Pages 339-356
Experiments with Spin Half Particles The Stern-Gerlach Experiment, Larmor Precession and Magnetic Resonance....Pages 357-388
Angular momentum III Eigenfunctions Using Operator Algebra....Pages 389-400
The Double Well Potential and the Kr?nig-Penney Model....Pages 401-422
The JWKB Approximation....Pages 423-477
Addition of Angular Momenta: The Clebsch-Gordan Coefficients....Pages 478-492
Time Independent Perturbation Theory....Pages 493-533
Effects of Magnetic Field....Pages 534-559
Front Matter....Pages 29-29
The Variational Method....Pages 560-578
The Helium Atom and the Exclusion Principle....Pages 579-597
Some Select Topics....Pages 598-624
Elementary Theory of Scattering....Pages 625-675
Time Dependent Perturbation Theory....Pages 676-715
The Semi-Classical Theory of Radiation and the Einstein Coefficients....Pages 716-741
The Quantum Theory of Radiation and its Interaction with Matter....Pages 742-778
Relativistic Theory....Pages 779-808
Back Matter....Pages 809-864

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An understanding of quantum mechanics is vital to all students of physics, chemistry and electrical engineering, but requires a lot of mathematical concepts, the details of which are given with great clarity in this book. Various concepts have been derived from first principles, so it can also be used for self-study. The chapters on the JWKB approximation, time-independent perturbation theory and effects of magnetic field stand out for their clarity and easy-to-understand mathematics. Two complete chapters on the linear harmonic oscillator provide a very detailed discussion of one of the most fundamental problems in quantum mechanics. Operator algebra is used to show the ease with which one can calculate the harmonic oscillator wave functions and study the evolution of the coherent state. Similarly, three chapters on angular momentum give a detailed account of this important problem. Perhaps the most attractive feature of the book is the excellent balance between theory and applications and the large number of applications in such diverse areas as astrophysics, nuclear physics, atomic and molecular spectroscopy, solid-state physics, and quantum well structures.
Content:
Front Matter....Pages i-xlviii
Front Matter....Pages 1-1
The Dirac Delta Function....Pages 3-18
Fourier Transforms....Pages 19-27
Front Matter....Pages 29-29
Particles and Waves and the Uncertainty Principle....Pages 31-70
Time Dependent Schr?dinger Equation....Pages 71-88
Propagation of Wave Packets and Concept of Group Velocity....Pages 89-114
Bound State Solutions of the Schr?dinger Equation....Pages 115-158
Linear Harmonic Oscillator: I Solution of the Schr?dinger Equation and Relationship with the Classical Oscillator....Pages 159-196
One-Dimensional Barrier Transmission Problems....Pages 197-220
Angular Momentum I—The Spherical Harmonics....Pages 221-244
Spherically Symmetric Potentials Hydrogen Atom Problem, Rotation Vibration Spectra, Three-Dimensional Oscillator....Pages 245-290
Dirac’s Bra and Ket Algebra....Pages 291-307
Linear Harmonic Oscillator II Solutions Using Bra and Ket Algebra....Pages 308-338
Angular Momentum II Using Bra and Ket Algebra....Pages 339-356
Experiments with Spin Half Particles The Stern-Gerlach Experiment, Larmor Precession and Magnetic Resonance....Pages 357-388
Angular momentum III Eigenfunctions Using Operator Algebra....Pages 389-400
The Double Well Potential and the Kr?nig-Penney Model....Pages 401-422
The JWKB Approximation....Pages 423-477
Addition of Angular Momenta: The Clebsch-Gordan Coefficients....Pages 478-492
Time Independent Perturbation Theory....Pages 493-533
Effects of Magnetic Field....Pages 534-559
Front Matter....Pages 29-29
The Variational Method....Pages 560-578
The Helium Atom and the Exclusion Principle....Pages 579-597
Some Select Topics....Pages 598-624
Elementary Theory of Scattering....Pages 625-675
Time Dependent Perturbation Theory....Pages 676-715
The Semi-Classical Theory of Radiation and the Einstein Coefficients....Pages 716-741
The Quantum Theory of Radiation and its Interaction with Matter....Pages 742-778
Relativistic Theory....Pages 779-808
Back Matter....Pages 809-864
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