Quantum Mechanics I. The Fundamentals 2nd Edition by S. Rajasekar 9781000729030 1000729036

Quantum Mechanics I. The Fundamentals 2nd Edition S. Rajasekar – Ebook Instant Download/Delivery ISBN(s): 9781000729030, 1000729036

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• ISBN 10:1000729036
• ISBN 13:9781000729030
• Author: S. Rajasekar 

Quantum Mechanics I
The Fundamentals

Table contents:

1 Why Was Quantum Mechanics Developed?
1.1 Introduction
1.2 Black Body Radiation
1.3 Photoelectric Effect
1.4 Hydrogen Spectrum
1.5 Franck–Hertz Experiment
1.6 Stern–Gerlach Experiment
1.7 Correspondence Principle
1.8 Compton Effect
1.9 Specific Heat Capacity
1.10 de Broglie Waves
1.11 Particle Diffraction
1.12 Wave-Particle Duality
1.13 Concluding Remarks
1.14 Bibliography
1.15 Exercises
2 Schrödinger Equation and Wave Function
2.1 Introduction
2.2 Construction of Schrödinger Equation
2.3 Solution of Time-Dependent Equation
2.4 Physical Interpretation of ψ*ψ
2.5 Conditions on Allowed Wave Functions
2.6 Box Normalization
2.7 A Special Feature of Occurrence of i in the Schrödinger Equation
2.8 Conservation of Probability
2.9 Expectation Value
2.10 Ehrenfest’s Theorem
2.11 Basic Postulates
2.12 Time Evolution of Stationary States
2.13 Conditions for Allowed Transitions
2.14 Orthogonality of Two States
2.15 Phase of the Wave Function
2.16 Classical Limit of Quantum Mechanics
2.17 Concluding Remarks
2.18 Bibliography
2.19 Exercises
3 Operators, Eigenvalues and Eigenfunctions
3.1 Introduction
3.2 Linear Operators
3.3 Commuting and Noncommuting Operators
3.4 Self-Adjoint and Hermitian Operators
3.5 Discrete and Continuous Eigenvalues
3.6 Meaning of Eigenvalues and Eigenfunctions
3.7 Parity Operator
3.8 Some Other Useful Operators
3.9 Concluding Remarks
3.10 Bibliography
3.11 Exercises
4 Exactly Solvable Systems I: Bound States
4.1 Introduction
4.2 Classical Probability Distribution
4.3 Free Particle
4.4 Harmonic Oscillator
4.5 Particle in the Potential V(x)=x2k, k=1,2,…
4.6 Particle in a Box
4.7 Morse Oscillator
4.8 Pöschl–Teller Potentials
4.9 Quantum Pendulum
4.10 Criteria for the Existence of a Bound State
4.11 Time-Dependent Harmonic Oscillator
4.12 Damped and Forced Linear Harmonic Oscillator
4.13 Two-Dimensional Systems
4.14 Rigid Rotator
4.15 Concluding Remarks
4.16 Bibliography
4.17 Exercises
5 Exactly Solvable Systems II: Scattering States
5.1 Introduction
5.2 Potential Barrier: Tunnel Effect
5.3 Finite Square-Well Potential
5.4 Potential Step
5.5 Locally Periodic Potential
5.6 Reflectionless Potentials
5.7 Dynamical Tunnelling
5.8 Concluding Remarks
5.9 Bibliography
5.10 Exercises
6 Matrix Mechanics
6.1 Introduction
6.2 Linear Vector Space and Tensor Products
6.3 Matrix Representation of Operators and Wave Function
6.4 Unitary Transformation
6.5 Schrödinger Equation and Other Quantities in Matrix Form
6.6 Application to Certain Systems
6.7 Dirac’s Bra and Ket Notations
6.8 Dimensions of Kets and Bras
6.9 Hilbert Space
6.10 Symmetry Operators in Hilbert Space
6.11 Projection and Displacement Operators
6.12 Quaternionic Quantum Mechanics
6.13 Concluding Remarks
6.14 Bibliography
6.15 Exercises
7 Various Pictures and Density Matrix
7.1 Introduction
7.2 Schrödinger Picture
7.3 Heisenberg Picture
7.4 Interaction Picture
7.5 Comparison of Three Representations
7.6 Density Matrix for a Single System
7.7 Density Matrix for an Ensemble
7.8 Time Evolution of Density Operator
7.9 Concluding Remarks
7.10 Bibliography
7.11 Exercises
8 Heisenberg Uncertainty Principle
8.1 Introduction
8.2 The Classical Uncertainty Relation
8.3 Heisenberg Uncertainty Relation
8.4 Condition for Minimum Uncertainty Product
8.5 Implications of Uncertainty Relation
8.6 Illustration of Uncertainty Relation
8.7 Some Extensions of Uncertainty Relation
8.8 The Modified Heisenberg Relation
8.9 Concluding Remarks
8.10 Bibliography
8.11 Exercises
9 Momentum Representation
9.1 Introduction
9.2 Momentum Eigenfunctions
9.3 Schrödinger Equation
9.4 Expressions for 〈X〉 and 〈p〉
9.5 Transformation Between Momentum and Coordinate Representations
9.6 Operators in Momentum Representation
9.7 Momentum Function of Some Systems
9.8 Concluding Remarks
9.9 Bibliography
9.10 Exercises
10 Wave Packet
10.1 Introduction
10.2 Phase and Group Velocities
10.3 Wave Packets and Uncertainty Principle
10.4 Gaussian Wave Packet
10.5 Wave Packet Revival
10.6 Almost Periodic Wave Packets
10.7 Concluding Remarks
10.8 Bibliography
10.9 Exercises
11 Theory of Angular Momentum
11.1 Introduction
11.2 Scalar Wave Function Under Rotations
11.3 Orbital Angular Momentum
11.4 Spin Angular Momentum
11.5 Spin-Orbit Coupling
11.6 Addition of Angular Momenta
11.7 Rotational Transformation of a Vector Wave Function and Spin
11.8 Rotational Properties of Vector Operators
11.9 Tensor Operators and the Wigner–Eckart Theorem
11.10 Concluding Remarks
11.11 Bibliography
11.12 Exercises
12 Hydrogen Atom
12.1 Introduction
12.2 Hydrogen Atom in Three-Dimension
12.3 Hydrogen Atom in D-Dimension
12.4 Field Produced by a Hydrogen Atom
12.5 System in Parabolic Coordinates
12.6 Concluding Remarks
12.7 Bibliography
12.8 Exercises
13 Approximation Methods I: Time-Independent Perturbation Theory
13.1 Introduction
13.2 Theory for Nondegenerate Case
13.3 Applications to Nondegenerate Levels
13.4 Theory for Degenerate Levels
13.5 First-Order Stark Effect in Hydrogen
13.6 Alternate Perturbation Theories
13.7 Concluding Remarks
13.8 Bibliography
13.9 Exercises
14 Approximation Methods II: Time-Dependent Perturbation Theory
14.1 Introduction
14.2 Transition Probability
14.3 Constant Perturbation
14.4 Harmonic Perturbation
14.5 Adiabatic Perturbation
14.6 Sudden Approximation
14.7 The Semiclassical Theory of Radiation
14.8 Concluding Remarks
14.9 Bibliography
14.10 Exercises
15 Approximation Methods III: WKB and Asymptotic Methods
15.1 Introduction
15.2 Principle of WKB Method
15.3 Applications of WKB Method
15.4 WKB Quantization with Perturbation
15.5 An Asymptotic Method
15.6 Concluding Remarks
15.7 Bibliography
15.8 Exercises
16 Approximation Methods IV: Variational Approach
16.1 Introduction
16.2 Calculation of Ground State Energy
16.3 Trial Eigenfunctions for Excited States
16.4 Application to Hydrogen Molecule
16.5 Hydrogen Molecule Ion
16.6 Concluding Remarks
16.7 Exercises
17 Scattering Theory
17.1 Introduction
17.2 Classical Scattering Cross-Section
17.3 Centre of Mass and Laboratory Coordinates Systems
17.4 Scattering Amplitude
17.5 Green’s Function Approach
17.6 Born Approximation
17.7 Partial Wave Analysis
17.8 Scattering from a Square-Well System
17.9 Phase-Shift of One-Dimensional Case
17.10 Inelastic Scattering
17.11 Concluding Remarks
17.12 Bibliography
17.13 Exercises
18 Identical Particles
18.1 Introduction
18.2 Permutation Symmetry
18.3 Symmetric and Antisymmetric Wave Functions
18.4 The Exclusion Principle
18.5 Spin Eigenfunctions of Two Electrons
18.6 Exchange Interaction
18.7 Excited States of the Helium Atom
18.8 Collisions Between Identical Particles
18.9 Uncertainty Principle for a System of Identical Particles
18.10 Concluding Remarks
18.11 Bibliography
18.12 Exercises
19 Relativistic Quantum Theory
19.1 Introduction
19.2 Klein–Gordon Equation
19.3 Dirac Equation for a Free Particle
19.4 Minimum Uncertainty Wave Packet
19.5 Spin of a Dirac Particle
19.6 Particle in a Potential
19.7 Klein Paradox
19.8 Relativistic Particle in a Box
19.9 Relativistic Hydrogen Atom
19.10 The Electron in a Field
19.11 Spin-Orbit Energy
19.12 Relativistic Quaternionic Quantum Mechanics
19.13 Concluding Remarks
19.14 Bibliography
19.15 Exercises
20 Mysteries in Quantum Mechanics
20.1 Introduction
20.2 The Collapse of the Wave Function
20.3 Einstein–Podolsky–Rosen (EPR) Paradox
20.4 Hidden Variables
20.5 The Paradox of Schrödinger’s Cat
20.6 Bell’s Theorem
20.7 Violation of Bell’s Theorem
20.8 Resolving EPR Paradox
20.9 Concluding Remarks
20.10 Bibliography
20.11 Exercises
21 Delayed-Choice Experiments
21.1 Introduction
21.2 Single Slit and Double Slit Experiments
21.3 Quantum Mechanical Explanation
21.4 Experiment With Mach–Zehnder Interferometer
21.5 Delayed-Choice Experiment
21.6 Delayed-Choice Quantum Eraser
21.7 Concluding Remarks
21.8 Bibliography
21.9 Exercises
22 Fractional Quantum Mechanics
22.1 Introduction
22.2 Integer and Fractional Diffusion Equations
22.3 Wave Function and Kernel
22.4 Space Fractional Schrödinger Equation
22.5 Solutions of Certain Space Fractional Schrödinger Equations
22.6 Fractional Schrödinger Equation in Relativistic Quantum Mechanics
22.7 Time Fractional Schrödinger Equation
22.8 Solutions of Certain Time Fractional Schrödinger Equations
22.9 Space-Time Fractional Schrödinger Equation
22.10 Concluding Remarks
22.11 Bibliography
22.12 Exercises
23 Numerical Methods for Quantum Mechanics
23.1 Introduction
23.2 Matrix Method for Computing Stationary State Solutions
23.3 Finite-Difference Time-Domain Method
23.4 Time-Dependent Schrödinger Equation
23.5 Quantum Scattering
23.6 Electronic Distribution of Hydrogen Atom
23.7 Schrödinger Equation with an External Field
23.8 Concluding Remarks
23.9 Bibliography
23.10 Exercises

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