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Principles of Quantum Mechanics : As Applied to Chemistry and Chemical Physics.

By: Publisher: Cambridge : Cambridge University Press, 1999Copyright date: ©1999Description: 1 online resource (364 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780511149054
Subject(s): Genre/Form: Additional physical formats: Print version:: Principles of Quantum Mechanics : As Applied to Chemistry and Chemical PhysicsDDC classification:
  • 541.2/8
LOC classification:
  • QD462 -- .F55 1999eb
Online resources:
Contents:
Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 1 The wave function -- 1.1 Wave motion -- Plane wave -- Composite wave -- Addition of two plane waves -- 1.2 Wave packet -- Gaussian wave number distribution -- Square pulse wave number distribution -- Uncertainty relation -- 1.3 Dispersion of a wave packet -- Gaussian wave packet -- 1.4 Particles and waves -- 1.5 Heisenberg uncertainty principle -- 1.6 Young's double-slit experiment -- 1.7 Stern-Gerlach experiment -- 1.8 Physical interpretation of the wave function -- Problems -- 2 Schrödinger wave mechanics -- 2.1 The Schrödinger equation -- 2.2 The wave function -- Interpretation -- Normalization -- Momentum-space wave function -- 2.3 Expectation values of dynamical quantities -- Ehrenfest's theorems -- Heisenberg uncertainty principle -- 2.4 Time-independent Schrödinger equation -- 2.5 Particle in a one-dimensional box -- 2.6 Tunneling -- 2.7 Particles in three dimensions -- Multi-particle system -- 2.8 Particle in a three-dimensional box -- Degeneracy of energy levels -- Problems -- 3 General principles of quantum theory -- 3.1 Linear operators -- 3.2 Eigenfunctions and eigenvalues -- Scalar product and orthogonality -- 3.3 Hermitian operators -- Eigenvalues -- Orthogonality theorem -- Extended orthogonality theorem -- 3.4 Eigenfunction expansions -- Completeness -- 3.5 Simultaneous eigenfunctions -- 3.6 Hilbert space and Dirac notation -- Bra vectors -- Projection operator -- 3.7 Postulates of quantum mechanics -- State function -- Physical quantities or observables -- Measurement of observable properties -- Collapse of the state function -- Time evolution of the state function -- 3.8 Parity operator -- 3.9 Hellmann-Feynman theorem -- 3.10 Time dependence of the expectation value -- 3.11 Heisenberg uncertainty principle -- Position-momentum uncertainty principle.
Minimum uncertainty wave packet -- Energy-time uncertainty principle -- Problems -- 4 Harmonic oscillator -- 4.1 Classical treatment -- 4.2 Quantum treatment -- Ladder operators -- Quantization of the energy -- Non-degeneracy of the energy levels -- 4.3 Eigenfunctions -- Lowering and raising operations -- Excited-state eigenfunctions -- Eigenfunctions in terms of Hermite polynomials -- Physical interpretation -- 4.4 Matrix elements -- 4.5 Heisenberg uncertainty relation -- 4.6 Three-dimensional harmonic oscillator -- Problems -- 5 Angular momentum -- 5.1 Orbital angular momentum -- Commutation relations -- 5.2 Generalized angular momentum -- Ladder operators -- Determination of the eigenvalues -- 5.3 Application to orbital angular momentum -- Ladder operators -- Normalization of… -- Spherical harmonics -- Relationship of spherical harmonics to associated Legendre polynomials -- 5.4 The rigid rotor -- 5.5 Magnetic moment -- Interaction with a magnetic field -- Problems -- 6 The hydrogen atom -- 6.1 Two-particle problem -- 6.2 The hydrogen-like atom -- 6.3 The radial equation -- Ladder operators -- Orthonormal properties of… -- Evaluation of the constants… -- Quantization of the energy -- Determination of the eigenfunctions -- Radial functions in terms of associated Laguerre polynomials -- Solution for positive energies -- Infinite nuclear mass -- 6.4 Atomic orbitals -- s orbitals -- p orbitals -- d orbitals -- Radial functions and expectation values -- 6.5 Spectra -- Pseudo-Zeeman effect -- Problems -- 7 Spin -- 7.1 Electron spin -- 7.2 Spin angular momentum -- 7.3 Spin one-half -- Pauli spin matrices -- 7.4 Spin-orbit interaction -- Problems -- 8 Systems of identical particles -- 8.1 Permutations of identical particles -- Two-particle systems -- Three-particle systems -- N-particle systems -- 8.2 Bosons and fermions -- 8.3 Completeness relation.
8.4 Non-interacting particles -- Probability densities -- Electron spin and the helium atom -- 8.5 The free-electron gas -- 8.6 Bose-Einstein condensation -- Problems -- 9 Approximation methods -- 9.1 Variation method -- Variation theorem -- Ground-state eigenfunction -- Example: particle in a box -- Example: harmonic oscillator -- Excited-state energies -- 9.2 Linear variation functions -- 9.3 Non-degenerate perturbation theory -- First-order corrections -- Second-order corrections -- Summary -- Relation to variation method -- 9.4 Perturbed harmonic oscillator -- 9.5 Degenerate perturbation theory -- 'Correct' zero-order eigenfunctions -- First-order corrections to the eigenfunctions -- Example: hydrogen atom in an electric field -- 9.6 Ground state of the helium atom -- Perturbation theory treatment -- Variation method treatment -- Problems -- 10 Molecular structure -- 10.1 Nuclear structure and motion -- Born-Oppenheimer approximation -- Born-Huang treatment -- 10.2 Nuclear motion in diatomic molecules -- Center-of-mass coordinates -- Electronic motion and the nuclear potential function -- Nuclear motion -- Higher-order approximation for nuclear motion -- Problems -- Appendix A Mathematical formulas -- Useful power series expansions -- Binomial expansions -- Useful integrals -- Integration by parts -- Gamma function -- Trigonometric functions -- Hyperbolic functions -- Schwarz's inequality -- Vector relations -- Spherical coordinates (r, Theta, Phi) -- Plane polar coordinates (r, Phi) -- Appendix B Fourier series and Fourier integral -- Fourier series -- Other variables -- Complex form -- Parseval's theorem -- Fourier integral -- Fourier integral in three dimensions -- Parseval's theorem -- Appendix C Dirac delta function -- Appendix D Hermite polynomials -- Recurrence relations -- Differential equation -- Integral relations -- Completeness.
Appendix E Legendre and associated Legendre polynomials -- Legendre polynomials -- Recurrence relations -- Differential equation -- Rodrigues' formula -- Associated Legendre polynomials -- Differential equation -- Orthogonality -- Normalization -- Completeness -- Appendix F Laguerre and associated Laguerre polynomials -- Laguerre polynomials -- Differential equation -- Associated Laguerre polynomials -- Differential equation -- Integral relations -- Completeness -- Appendix G Series solutions of differential equations -- General procedure -- Applications -- Harmonic oscillator -- Orbital angular momentum -- Radial equation for the hydrogen-like atom -- Appendix H Recurrence relation for hydrogen-atom expectation values -- Appendix I Matrices -- Matrix algebra -- Square matrices -- Determinants -- Special square matrices -- Linear vector space -- Eigenvalues -- Trace -- Appendix J Evaluation of the two-electron interaction integral -- Selected bibliography -- Applied mathematical methods -- Undergraduate physical chemistry -- History and philosophy of quantum theory -- Some 'classic' quantum mechanics texts -- Some recent quantum mechanics texts -- Angular momentum -- Atoms and atomic spectra -- More advanced applications of quantum mechanics -- Compilations of problems in quantum mechanics -- Index.
Summary: Graduate-level text in quantum mechanics for chemists and chemical physicists.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan Available EBKAF0005692
Ebrary Ebrary Algeria Available
Ebrary Ebrary Cyprus Available
Ebrary Ebrary Egypt Available
Ebrary Ebrary Libya Available
Ebrary Ebrary Morocco Available
Ebrary Ebrary Nepal Available EBKNP0005692
Ebrary Ebrary Sudan Available
Ebrary Ebrary Tunisia Available
Total holds: 0

Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 1 The wave function -- 1.1 Wave motion -- Plane wave -- Composite wave -- Addition of two plane waves -- 1.2 Wave packet -- Gaussian wave number distribution -- Square pulse wave number distribution -- Uncertainty relation -- 1.3 Dispersion of a wave packet -- Gaussian wave packet -- 1.4 Particles and waves -- 1.5 Heisenberg uncertainty principle -- 1.6 Young's double-slit experiment -- 1.7 Stern-Gerlach experiment -- 1.8 Physical interpretation of the wave function -- Problems -- 2 Schrödinger wave mechanics -- 2.1 The Schrödinger equation -- 2.2 The wave function -- Interpretation -- Normalization -- Momentum-space wave function -- 2.3 Expectation values of dynamical quantities -- Ehrenfest's theorems -- Heisenberg uncertainty principle -- 2.4 Time-independent Schrödinger equation -- 2.5 Particle in a one-dimensional box -- 2.6 Tunneling -- 2.7 Particles in three dimensions -- Multi-particle system -- 2.8 Particle in a three-dimensional box -- Degeneracy of energy levels -- Problems -- 3 General principles of quantum theory -- 3.1 Linear operators -- 3.2 Eigenfunctions and eigenvalues -- Scalar product and orthogonality -- 3.3 Hermitian operators -- Eigenvalues -- Orthogonality theorem -- Extended orthogonality theorem -- 3.4 Eigenfunction expansions -- Completeness -- 3.5 Simultaneous eigenfunctions -- 3.6 Hilbert space and Dirac notation -- Bra vectors -- Projection operator -- 3.7 Postulates of quantum mechanics -- State function -- Physical quantities or observables -- Measurement of observable properties -- Collapse of the state function -- Time evolution of the state function -- 3.8 Parity operator -- 3.9 Hellmann-Feynman theorem -- 3.10 Time dependence of the expectation value -- 3.11 Heisenberg uncertainty principle -- Position-momentum uncertainty principle.

Minimum uncertainty wave packet -- Energy-time uncertainty principle -- Problems -- 4 Harmonic oscillator -- 4.1 Classical treatment -- 4.2 Quantum treatment -- Ladder operators -- Quantization of the energy -- Non-degeneracy of the energy levels -- 4.3 Eigenfunctions -- Lowering and raising operations -- Excited-state eigenfunctions -- Eigenfunctions in terms of Hermite polynomials -- Physical interpretation -- 4.4 Matrix elements -- 4.5 Heisenberg uncertainty relation -- 4.6 Three-dimensional harmonic oscillator -- Problems -- 5 Angular momentum -- 5.1 Orbital angular momentum -- Commutation relations -- 5.2 Generalized angular momentum -- Ladder operators -- Determination of the eigenvalues -- 5.3 Application to orbital angular momentum -- Ladder operators -- Normalization of… -- Spherical harmonics -- Relationship of spherical harmonics to associated Legendre polynomials -- 5.4 The rigid rotor -- 5.5 Magnetic moment -- Interaction with a magnetic field -- Problems -- 6 The hydrogen atom -- 6.1 Two-particle problem -- 6.2 The hydrogen-like atom -- 6.3 The radial equation -- Ladder operators -- Orthonormal properties of… -- Evaluation of the constants… -- Quantization of the energy -- Determination of the eigenfunctions -- Radial functions in terms of associated Laguerre polynomials -- Solution for positive energies -- Infinite nuclear mass -- 6.4 Atomic orbitals -- s orbitals -- p orbitals -- d orbitals -- Radial functions and expectation values -- 6.5 Spectra -- Pseudo-Zeeman effect -- Problems -- 7 Spin -- 7.1 Electron spin -- 7.2 Spin angular momentum -- 7.3 Spin one-half -- Pauli spin matrices -- 7.4 Spin-orbit interaction -- Problems -- 8 Systems of identical particles -- 8.1 Permutations of identical particles -- Two-particle systems -- Three-particle systems -- N-particle systems -- 8.2 Bosons and fermions -- 8.3 Completeness relation.

8.4 Non-interacting particles -- Probability densities -- Electron spin and the helium atom -- 8.5 The free-electron gas -- 8.6 Bose-Einstein condensation -- Problems -- 9 Approximation methods -- 9.1 Variation method -- Variation theorem -- Ground-state eigenfunction -- Example: particle in a box -- Example: harmonic oscillator -- Excited-state energies -- 9.2 Linear variation functions -- 9.3 Non-degenerate perturbation theory -- First-order corrections -- Second-order corrections -- Summary -- Relation to variation method -- 9.4 Perturbed harmonic oscillator -- 9.5 Degenerate perturbation theory -- 'Correct' zero-order eigenfunctions -- First-order corrections to the eigenfunctions -- Example: hydrogen atom in an electric field -- 9.6 Ground state of the helium atom -- Perturbation theory treatment -- Variation method treatment -- Problems -- 10 Molecular structure -- 10.1 Nuclear structure and motion -- Born-Oppenheimer approximation -- Born-Huang treatment -- 10.2 Nuclear motion in diatomic molecules -- Center-of-mass coordinates -- Electronic motion and the nuclear potential function -- Nuclear motion -- Higher-order approximation for nuclear motion -- Problems -- Appendix A Mathematical formulas -- Useful power series expansions -- Binomial expansions -- Useful integrals -- Integration by parts -- Gamma function -- Trigonometric functions -- Hyperbolic functions -- Schwarz's inequality -- Vector relations -- Spherical coordinates (r, Theta, Phi) -- Plane polar coordinates (r, Phi) -- Appendix B Fourier series and Fourier integral -- Fourier series -- Other variables -- Complex form -- Parseval's theorem -- Fourier integral -- Fourier integral in three dimensions -- Parseval's theorem -- Appendix C Dirac delta function -- Appendix D Hermite polynomials -- Recurrence relations -- Differential equation -- Integral relations -- Completeness.

Appendix E Legendre and associated Legendre polynomials -- Legendre polynomials -- Recurrence relations -- Differential equation -- Rodrigues' formula -- Associated Legendre polynomials -- Differential equation -- Orthogonality -- Normalization -- Completeness -- Appendix F Laguerre and associated Laguerre polynomials -- Laguerre polynomials -- Differential equation -- Associated Laguerre polynomials -- Differential equation -- Integral relations -- Completeness -- Appendix G Series solutions of differential equations -- General procedure -- Applications -- Harmonic oscillator -- Orbital angular momentum -- Radial equation for the hydrogen-like atom -- Appendix H Recurrence relation for hydrogen-atom expectation values -- Appendix I Matrices -- Matrix algebra -- Square matrices -- Determinants -- Special square matrices -- Linear vector space -- Eigenvalues -- Trace -- Appendix J Evaluation of the two-electron interaction integral -- Selected bibliography -- Applied mathematical methods -- Undergraduate physical chemistry -- History and philosophy of quantum theory -- Some 'classic' quantum mechanics texts -- Some recent quantum mechanics texts -- Angular momentum -- Atoms and atomic spectra -- More advanced applications of quantum mechanics -- Compilations of problems in quantum mechanics -- Index.

Graduate-level text in quantum mechanics for chemists and chemical physicists.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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