This lively textbook differs from others on the subject by its usefulness as a conceptual and mathematical preparation for the study of quantum mechanics, by its emphasis on a variety of learning tools aimed at fostering the student's self-awareness of learning, and by its frequent connections to current research. INDICE: Learning tools used in this book; 1.: Simple Harmonic Motion; 1.1 Sinusoidal Oscillations are Everywhere; 1.2 The physics and mathematics behind simple harmonic motion; 1.3 Important parameters and adjustable constant of simple harmonic motion; 1.4 Mass on a spring; 1.5 Electrical oscillators; 1.6 Review of Taylor Series Approximations; 1.7 Euler's equation; 1.8 Review of complex numbers; 1.9 Complex exponential notation for oscillatory motion; 1.10The complex representation for AC circuits; 1.11 Another important complex function: The quantum mechanical wavefunction; 1.12 Pure sinusoidal oscillationsand uncertainty principles; Concept and skill inventory; Problems; 2.: Examples of Simple Harmonic Motion; 2.1 Requirements for harmonic oscillation; 2.2 Pendulums; 2.3 Elastic deformations and Young's modulus; 2.4 Shear; 2.5 Torsionand Torsional Oscillators; 2.6 Bending and Cantilevers; Concept and skill inventory; Problems; 3.: Damped oscillations; 3.1 Damped mechanical oscillators; 3.2 Damped electrical oscillators; 3.3 Exponential decay of energy; 3.4 The Quality Factor; 3.5 Underdamped, overdamped, and critically damped behavior; 3.6Types of damping; Concept and skill inventory; Problems; 4.: Driven Oscillations and Resonance; 4.1 Resonance; 4.2 Effects of damping; 4.3 Energy flow; 4.4Linear differential equations, the superposition principle for driven systems, and the response to multiple drive forces; 4.5 Transients; 4.6 Electrical resonance; 4.7 Other examples of resonance: MRI and other spectroscopies; 4.8 Non-linear oscillators and chaos; Concept and skill inventory; Problems; 5.: Symmetric coupled oscillators and Hilbert space; 5.1 Beats: An aside?; 5.2 Two symmetric coupled oscillators: equations of motion; 5.3 Normal modes; 5.4 Superposing normal modes; 5.5 Normal mode analysis, and normal modes as an alternatedescription of reality; 5.6 Hilbert Space and bra-ket notation; 5.7 The analogy between coupled oscillators and molecular energy levels; 5.8 Non-zero initial velocities; 5.9 Damped, driven coupled oscillators; Concept and skill inventory; Problems; 6.: Asymmetric coupled oscillators and the eigenvalue equation; 6.1 Matrix math; 6.2 Equations of motion and the eigenvalue equation; 6.3 Procedure for solving the eigenvalue equation; 6.4 Systems with more than two objects; 6.5 Normal mode analysis for mulit-object, asymmetrical systems; 6.6 More matrix math; 6.7 Orthogonality of normal modes, normal mode coordinates, degeneracy, and scaling of Hilbert space for unequal masses; Concept and skill inventory; Problems; 7.: String theory; 7.1 The beaded string; 7.2 Standing wave guess: Boundary conditions quantize the allowed frequencies; 7.3 The highestpossible frequency; connection to waves in a crystalline solid; 7.4 Normal mode analysis for the beaded string; 7.5 Longitudinal oscillations; 7.6 The continuous string; 7.7 Normal mode analysis for continuous systems; 7.8 k-space; Concept and skill inventory; Problems;
- ISBN: 978-0-19-539349-1
- Editorial: Oxford University
- Encuadernacion: Cartoné
- Páginas: 416
- Fecha Publicación: 10/06/2010
- Nº Volúmenes: 1
- Idioma: Inglés