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Quantum Mechanics. A Conceptual Approach

  • ID: 2178315
  • Book
  • 208 Pages
  • John Wiley and Sons Ltd
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A unique introductory text on quantum mechanics

Albert Einstein famously expressed his dismay at the implications of quantum mechanics (QM) when he protested, "God does not play dice with the universe." Theology aside, QM theory has held up as a scientific explanation of matter and radiation at the atomic level. Along with Einstein’s Theory of General Relativity, QM comprises the backbone of modern physics and plays a majo role in our understanding of chemistry.

Quantum Mechanics: A Conceptual Approach offers students an easy–to–understand introduction to this essential field. Assuming no prior knowledge on the part of its reader, this text emphasizes the basic concepts that provide a solid foundation for the future study of quantum chemistry. Beginning with a description of the historical developments that led to the discovery of QM, a feature often neglected in other texts, Quantum Mechanics moves on to cover:

  • Mathematics of QM Applications
  • Classical mechanics
  • The hydrogen atom
  • Wave mechanics of a free particle
  • Atomic structure
  • The Schrödinger equation
  • Molecular structure

Written in a student–friendly style by experienced author and professor Hendrik Hameka, this text also includes problem sets to reinforce the concepts outlined. Both comprehensive and accessible, Quantum Mechanics: A Conceptual Approach provides all those interested in the field with an invaluable introduction to this important topic.

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1. The Discovery of Quantum Mechanics.

I Introduction.

II Planck and Quantization.

III Bohr and the Hydrogen Atom.

IV Matrix Mechanics.

V The Uncertainty Relations.

VI Wave Mechanics.

VII The Final Touches of Quantum Mechanics.

VIII Concluding Remarks.

2. The Mathematics of Quantum Mechanics.

I Introduction.

II Differential Equations.

III Kummer s Function.

IV Matrices.

V Permutations.

VI Determinants.

VII Properties of Determinants.

VIII Linear Equations and Eigenvalues.

IX Problems.

3. Classical Mechanics.

I Introduction.

II Vectors and Vector Fields.

III Hamiltonian Mechanics.

IV The Classical Harmonic Oscillator.

V Angular Momentum.

VI Polar Coordinates.

VII Problems.

4. Wave Mechanics of a Free Particle.

I Introduction.

II The Mathematics of Plane Waves.

III The Schrödinger Equation of a Free Particle.

IV The Interpretation of the Wave Function.

V Wave Packets.

VI Concluding Remarks.

VII Problems.

5. The Schrödinger Equation.

I Introduction.

II Operators.

III The Particle in a Box.

IV Concluding Remarks.

V Problems.

6. Applications.

I Introduction.

II A Particle in a Finite Box.

III Tunneling.

IV The Harmonic Oscillator.

V Problems.

7. Angular Momentum.

I Introduction.

II Commuting Operators.

III Commutation Relations of the Angular Momentum.

IV The Rigid Rotor.

V Eigenfunctions of the Angular Momentum.

VI Concluding Remarks.

VII Problems.

8. The Hydrogen Atom.

I Introduction.

II Solving the Schrödinger Equation.

III Deriving the Energy Eigenvalues.

IV The Behavior of the Eigenfunctions.

V Problems.

9. Approximate Methods.

I Introduction.

II The Variational Principle.

III Applications of the Variational Principle.

IV Perturbation Theory for a Nondegenerate State.

V The Stark Effect of the Hydrogen Atom.

VI Perturbation Theory for Degenerate States.

VII Concluding Remarks.

VIII Problems.

10. The Helium Atom.

I Introduction.

II Experimental Developments.

III Pauli s Exclusion Principle.

IV The Discovery of the Electron Spin.

V The Mathematical Description of the Electron Spin.

VI The Exclusion Principle Revisited.

VII Two–Electron Systems.

VIII The Helium Atom.

IX The Helium Atom Orbitals.

X Concluding Remarks.

XI Problems.

11 Atomic Structure.

I Introduction.

II Atomic and Molecular Wave Function.

III The Hartree–Fock Method.

IV Slater Orbitals.

V Multiplet Theory.

VI Concluding Remarks.

VII Problems.

12 Molecular Structure.

I Introduction.

II The Born–Oppenheimer Approximation.

III Nuclear Motion of Diatomic Molecules.

IV The Hydrogen Molecular Ion.

V The Hydrogen Molecule.

VI The Chemical Bond.

VII The Structures of Some Simple Polyatomic Molecules.

VIII The Hückel Molecular Orbital Method.

IX Problems.


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Hendrik F. Hameka
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