A concise introduction to quantum mechanics / Mark S. Swanson.

Περιλαμβάνει βιβλιογραφικές παραπομπές.

1. Classical mechanics and electromagnetism -- 1.1. Newtonian mechanics -- 1.2. Light and electromagnetism -- 1.3. Properties of Newtonian point particle solutions

2. The origins of quantum mechanics -- 2.1. Blackbody radiation and Planck's constant -- 2.2. The photoelectric effect and photons -- 2.3. Electron diffraction and the de Broglie wavelength -- 2.4. Bohr's atom

3. The wave function -- 3.1. Basic properties of the wave function -- 3.2. Complex variables -- 3.3. The complex wave function -- 3.4. Fourier series and function spaces -- 3.5. The one-dimensional box

4. Wave mechanics -- 4.1. The Schr�odinger equation and its general properties -- 4.2. Observables and the wave function -- 4.3. The Heisenberg uncertainty principle -- 4.4. Wave packets

5. Applications of wave mechanics -- 5.1. Barrier reflection and tunneling -- 5.2. The one-dimensional harmonic oscillator -- 5.3. The hydrogen atom -- 5.4. Electromagnetic interactions

6. Dirac notation, operators, and matrices -- 6.1. Hilbert space -- 6.2. Hilbert space and Dirac notation -- 6.3. Matrices and basic linear algebra -- 6.4. Representations of quantum mechanics -- 6.5. The linear potential in momentum space -- 6.6. Operator techniques in quantum mechanics -- 6.7. Matrix representations of quantum mechanics -- 6.8. Two state oscillations -- 6.9. Electron diffraction revisited

7. Angular momentum, spin, and statistics -- 7.1. Symmetry operations -- 7.2. Rotation group theory -- 7.3. Rotations and quantum mechanics -- 7.4. General angular momentum -- 7.5. Electron spin and spinor representations -- 7.6. Multiparticle states and statistics -- 7.7. Angular momentum addition -- 8. Bibliography.

Assuming a background in basic classical physics, multivariable calculus, and differential equations, A Concise Introduction to Quantum Mechanics provides a self-contained presentation of the mathematics and physics of quantum mechanics. The relevant aspects of classical mechanics and electrodynamics are reviewed, and the basic concepts of wave-particle duality are developed as a logical outgrowth of experiments involving blackbody radiation, the photoelectric effect, and electron diffraction. The Copenhagen interpretation of the wave function and its relation to the particle probability density is presented in conjunction with Fourier analysis and its generalization to function spaces. These concepts are combined to analyze the system consisting of a particle confined to a box, developing the probabilistic interpretation of observations and their associated expectation values. The Schr�odinger equation is then derived by using these results and demanding both Galilean invariance of the probability density and Newtonian energy-momentum relations. The general properties of the Schr�odinger equation and its solutions are analyzed, and the theory of observables is developed along with the associated Heisenberg uncertainty principle. Basic applications of wave mechanics are made to free wave packet spreading, barrier penetration, the simple harmonic oscillator, the Hydrogen atom, and an electric charge in a uniform magnetic field. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented and used to analyze coherent states, the linear potential, two state oscillations, and electron diffraction. Applications are made to photon and electron spin and the addition of angular momentum, and direct product multiparticle states are used to formulate both the Pauli exclusion principle and quantum decoherence. The book concludes with an introduction to the rotation group and the general properties of angular momentum.