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Quantum mechanics /

Quantum mechanics is one of the most brilliant and exciting theories of the 20th century. It has not only explained a wide range of phenomena but has brought revolutionary changes in the conceptual foundations of physics and continues to shape the modern world. As quantum mechanics involves the intr...

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Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Saleem, Mohammad (Autor)
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2015]
Colección:	IOP (Series). Release 2. IOP expanding physics.
Temas:	Quantum theory. SCIENCE / Physics / Quantum Theory. Quantum physics (quantum mechanics & quantum field theory)
Acceso en línea:	Texto completo

Tabla de Contenidos:

Preface
Author biography
1. The failure of classical physics and the advent of quantum mechanics
1.1. A challenge for classical physics
1.2. The photoelectric effect
1.3. The Compton effect
1.4. Heisenberg's uncertainty principle
1.5. The correspondence principle
1.6. The Schrödinger wave equation
1.7. Constraints on solutions
1.8. Eigenfunctions and eigenvalues
1.9. The principle of superposition
1.10. Complementarity
1.11. Schrödinger's amplitude equation
1.12. The orthonormal set of functions
1.13. The equation of continuity
1.14. Complete sets of functions
1.15. The quantum theory of measurement
1.16. Observables and expectation values
1.17. Phases and relative phases
1.18. Postulates of quantum mechanics
1.19. The Schrödinger wave equation under space reflection, space inversion and time reversal
1.20. Concluding remarks
2. A particle in a one-dimensional box
2.1. Introduction
2.2. The solution of Schrödinger's amplitude equation
2.3. Zero-point energy
2.4. The normalisation constant
2.5. The parity of eigenfunctions
3. Free particles
3.1. Introduction
3.2. Free particles
3.3. Normalisation of stationary wave solutions
3.4. Normalisation of progressive wave solutions
3.5. Dirac's delta function
3.6. Continuous distribution of eigenvalues and Dirac's delta function
3.7. Eigenfunctions and eigenvalues of the position operator
3.8. Eigenfunctions and eigenvalues of the momentum operator
3.9. Normalisation of a free particle eigenfunction using a delta function
4. Linear harmonic oscillator
4.1. Classical theory
4.2. Quantum theory
4.3. The asymptotic solution
4.4. The general solution
4.5. A physically acceptable solution
4.6. Energy eigenvalues
4.7. Hermite polynomials
4.8. The normalisation process
4.9. Probability distributions
4.10. The importance of the harmonic oscillator
4.11. Parity
5. The role of Hermitian operators
5.1. Linear operators
5.2. Hermitian operators
5.3. The closure relation
5.4. Constants of motion
5.5. The classical limit of quantum mechanics : the Ehrenfest theorem
5.6. The virial theorem
5.7. Heisenberg's uncertainty principle
5.8. The parity operator
5.9. Antilinear operators
5.10. Antiunitary operators
6. Potentials with finite discontinuities
6.1. Potential steps
6.2. The potential barrier
6.3. [alpha]-particle decay
6.4. The square-well potential
7. Spherically symmetric potentials
7.1. Introduction
7.2. Spherically symmetric potentials
7.3. Separation of variables
7.4. Solution of the differential equation for F([phi])
7.5. Solution of the differential equation for P([theta])
7.6. Legendre polynomials and associated Legendre functions
7.7. Spherical harmonics
7.8. Hydrogen and hydrogenic atoms
7.9. The solution of the radial equation
7.10. Physically acceptable solutions for the radial equation and discrete energy values
7.11. The parity of a particle in a spherically symmetric potential
7.12. Comparison of the spectral series of hydrogen atom with experiments
7.13. The radial wave function
7.14. The spectroscopic notation
7.15. The normalised solution for the hydrogenic atom
7.16. Stationary states
8. Matrix mechanics
8.1. Matrix representation of an operator
8.2. Change of basis and unitary transformation
8.3. Coordinate and momentum representations
8.4. Continuous distribution of eigenvalues
9. Angular momentum
9.1. Angular momentum operator
9.2. Commutators of various components of L
9.3. Commutator of L2 and Lz
9.4. Components of the orbital angular momentum operator in spherical polar coordinates
9.5. L2 in spherical polar coordinates
9.6. Eigenfunctions and eigenvalues of Lz
9.7. Eigenvalues of Lz and L2 corresponding to their simultaneous eigenfunctions and ladder operators
9.8. Normal Zeeman effect
9.9. General theory of angular momentum
9.10. Characteristics of ladder operators
9.11. Electron spin
9.12. Matrix representations of Sx, Sy, Sz
9.13. Eigenvectors of Sz
9.14. The wave function for the electron
9.15. Spins of elementary particles
9.16. The average value of spin
9.17. Spin and statistics
9.18. Addition of angular momenta
9.19. Clebsch-Gordan coefficients
10. Perturbation theory
10.1. Introduction
10.2. Time-independent perturbation theory for nondegenerate states
10.3. First-order correction to energy
10.4. The anomalous Zeeman effect
10.5. The first-order correction to the eigenfunction
10.6. Second-order non-degenerate perturbation
10.7. The second-order correction to energy
10.8. The second-order correction to the eigenfunction
10.9. First-order perturbation : energy correction in a two-fold degenerate case
10.10. The application of perturbation theory to the Stark effect
10.11. Time-dependent perturbation theory
10.12. Harmonic perturbation
10.13. Fermi's golden rule
11. Theory of elastic scattering
11.1. Introduction
11.2. Centre-of-mass and laboratory frames of reference
11.3. The effect of collision on the velocity of the centre-of-mass in the laboratory frame
11.4. Relation between scattering angles in the laboratory and centre-of-mass frames
11.5. Relation between differential cross sections in the laboratory and centre-of-mass frames
11.6. Scattering by a stationary target
11.7. Relation between the scattering amplitude and differential cross section
11.8. Computation of the scattering amplitude
11.9. The Born approximation
11.10. Scattering of high energy electrons by a screened Coulomb potential
11.11. Partial wave analysis
11.12. The incident particle wave in terms of partial waves
11.13. Phase shift and scattering
11.14. A general solution in terms of partial waves
11.15. Optical theorem
11.16. Scattering by a hard sphere
11.17. Scattering from a potential square well
11.18. s-wave scattering for a square-well potential
11.19. Resonance scattering
11.20. Zero-energy scattering and the scattering length
11.21. Identical particles
12. Dirac's formalism
12.1. Introduction
12.2. Unitary operators
12.3. Unitary transformation
12.4. A particular unitary operator
12.5 Representations and change of basis
12.6. A one-dimensional oscillator
12.7. The relation between state vectors and wave functions
12.8. A free particle.

Quantum mechanics /

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