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Computational Physics: Simulation of Classical and Quantum Systems [Multiple-component retail product]

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  • Formaat: Multiple-component retail product, 310 pages, kõrgus x laius: 235x155 mm, kaal: 728 g, 116 black & white illustrations
  • Ilmumisaeg: 30-Nov-2010
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642139892
  • ISBN-13: 9783642139895
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  • Multiple-component retail product
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Computational Physics: Simulation of Classical and Quantum SystemsSuurem pilt
  • Formaat: Multiple-component retail product, 310 pages, kõrgus x laius: 235x155 mm, kaal: 728 g, 116 black & white illustrations
  • Ilmumisaeg: 30-Nov-2010
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642139892
  • ISBN-13: 9783642139895
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783642139895.html
Märksõnad:
Computational Physics introduces the basic numerical methods behind computational physics, providing computer experiments that demonstrate each algorithm. The simulation of classical and quantum systems is also included, with instructive examples spanning many fields in physics.

This book encapsulates the coverage for a two-semester course in computational physics. The first part introduces the basic numerical methods while omitting mathematical proofs but demonstrating the algorithms by way of numerous computer experiments. The second part specializes in simulation of classical and quantum systems with instructive examples spanning many fields in physics, from a classical rotor to a quantum bit. All program examples are realized as Java applets ready to run in your browser and do not require any programming skills.
Part I Numerical Methods
1 Error Analysis
3(12)
1.1 Machine Numbers and Rounding Errors
3(3)
1.2 Numerical Errors of Elementary Floating Point Operations
6(2)
1.2.1 Numerical Extinction
6(1)
1.2.2 Addition
7(1)
1.2.3 Multiplication
8(1)
1.3 Error Propagation
8(3)
1.4 Stability of Interative Algorithms
11(1)
1.5 Example: Rotation
12(1)
1.6 Truncation Error
13(2)
Problems
13(2)
2 Interpolation
15(14)
2.1 Interpolating Functions
15(1)
2.2 Polynomial Interpolation
16(5)
2.2.1 Lagrange Polynomials
16(1)
2.2.2 Newton's Divided Differences
17(1)
2.2.3 Interpolation Error
18(2)
2.2.4 Neville Method
20(1)
2.3 Spline Interpolation
21(4)
2.4 Multivariate Interpolation
25(4)
Problems
26(3)
3 Numerical Differentiation
29(8)
3.1 Simple Forward Difference
29(1)
3.2 Symmetrical Difference Quotient
30(1)
3.3 Extrapolation Methods
31(2)
3.4 Higher Derivatives
33(1)
3.5 More Dimensions
34(3)
Problems
35(2)
4 Numerical Integration
37(10)
4.1 Equidistant Sample Points
37(5)
4.1.1 Newton-Cotes Rules
38(1)
4.1.2 Newton-Cotes Expressions for an Open Interval
39(1)
4.1.3 Composite Newton-Cotes Formulas
40(1)
4.1.4 Extrapolation Method (Romberg Integration)
40(2)
4.2 Optimized Sample Points
42(5)
4.2.1 Clenshaw-Curtis Expressions
42(1)
4.2.2 Gaussian Integration
43(2)
Problems
45(2)
5 Systems of Inhomogeneous Linear Equations
47(16)
5.1 Gaussian Elimination Method
47(4)
5.1.1 Pivoting
50(1)
5.1.2 Direct LU Decomposition
51(1)
5.2 QR Decomposition
51(2)
5.3 Linear Equations with Tridiagonal Matrix
53(2)
5.4 Cyclic Tridiagonal Systems
55(1)
5.5 Iterative Solution of Inhomogeneous Linear Equations
56(3)
5.5.1 General Treatment
56(1)
5.5.2 Jacobi Method
57(1)
5.5.3 Gauss-Seidel Method
57(1)
5.5.4 Damping and Successive Over-Relaxation
58(1)
5.6 Conjugate Gradients
59(4)
Problems
60(3)
6 Roots and Extremal Points
63(10)
6.1 Root Finding
63(4)
6.1.1 Bisection
63(1)
6.1.2 Regula Falsi Method
64(1)
6.1.3 Newton-Raphson Method
65(1)
6.1.4 Secant Method
66(1)
6.1.5 Roots of Vector Functions
66(1)
6.2 Optimization Without Constraints
67(6)
6.2.1 Steepest Descent Method
68(1)
6.2.2 Conjugate Gradient Method
68(1)
6.2.3 Newton-Raphson Method
69(1)
6.2.4 Quasi-Newton Methods
69(1)
Problems
70(3)
7 Fourier Transformation
73(14)
7.1 Discrete Fourier Transformation
74(4)
7.1.1 Trigonometric Interpolation
75(2)
7.1.2 Real-Valued Functions
77(1)
7.1.3 Approximate Continuous Fourier Transformation
77(1)
7.2 Algorithms
78(9)
7.2.1 Goertzel's Algorithm
79(1)
7.2.2 Fast Fourier Transformation
80(4)
Problems
84(3)
8 Random Numbers and Monte Carlo Methods
87(22)
8.1 Some Basic Statistics
87(8)
8.1.1 Probability Density and Cumulative Probability Distribution
87(1)
8.1.2 Expectation Values and Moments
88(4)
8.1.3 Multivariate Distributions
92(1)
8.1.4 Central Limit Theorem
93(1)
8.1.5 Example: Binomial Distribution
93(1)
8.1.6 Average of Repeated Measurements
94(1)
8.2 Random Numbers
95(4)
8.2.1 The Method by Marsaglia and Zamann
96(1)
8.2.2 Random Numbers with Given Distribution
96(1)
8.2.3 Examples
97(2)
8.3 Monte Carlo Integration
99(3)
8.3.1 Numerical Calculation of π
99(1)
8.3.2 Calculation of an Integral
100(1)
8.3.3 More General Random Numbers
101(1)
8.4 Monte Carlo Method for Thermodynamic Averages
102(7)
8.4.1 Simple (Minded) Sampling
102(1)
8.4.2 Importance Sampling
103(1)
8.4.3 Metropolis Algorithm
104(2)
Problems
106(3)
9 Eigenvalue Problems
109(8)
9.1 Direct Solution
109(1)
9.2 Jacobi Method
109(2)
9.3 Tridiagonal Matrices
111(1)
9.4 Reduction to a Tridiagonal Matrix
111(3)
9.5 Large Matrices
114(3)
Problems
115(2)
10 Data Fitting
117(12)
10.1 Least Square Fit
117(6)
10.1.1 Linear Least Square Fit
119(1)
10.1.2 Least Square Fit Using Orthogonalization
120(3)
10.2 Singular Value Decomposition
123(6)
Problems
127(2)
11 Equations of Motion
129(28)
11.1 State Vector of a Physical System
129(1)
11.2 Time Evolution of the State Vector
130(2)
11.3 Explicit Forward Euler Method
132(2)
11.4 Implicit Backward Euler Method
134(1)
11.5 Improved Euler Methods
135(2)
11.6 Taylor Series Methods
137(1)
11.7 Runge-Kutta Methods
138(2)
11.7.1 Second-Order Runge-Kutta Method
138(1)
11.7.2 Third-Order Runge-Kutta Method
138(1)
11.7.3 Fourth-Order Runge-Kutta Method
139(1)
11.8 Quality Control and Adaptive Step-Size Control
140(1)
11.9 Extrapolation Methods
141(1)
11.10 Multistep Methods
142(2)
11.10.1 Explicit Multistep Methods
142(1)
11.10.2 Implicit Multistep Methods
143(1)
11.10.3 Predictor-Corrector Methods
144(1)
11.11 Verlet Methods
144(13)
11.11.1 Liouville Equation
144(1)
11.11.2 Split Operator Approximation
145(1)
11.11.3 Position Verlet Method
146(1)
11.11.4 Velocity Verlet Method
146(1)
11.11.5 Standard Verlet Method
147(2)
11.11.6 Error Accumulation for the Standard Verlet Method
149(1)
11.11.7 Leap Frog Method
149(1)
Problems
150(7)
Part II Simulation of Classical and Quantum Systems
12 Rotational Motion
157(22)
12.1 Transformation to a Body Fixed Coordinate System
157(1)
12.2 Properties of the Rotation Matrix
158(2)
12.3 Properties of W, Connection with the Vector of Angular Velocity
160(1)
12.4 Transformation Properties of the Angular Velocity
161(2)
12.5 Momentum and Angular Momentum
163(1)
12.6 Equations of Motion of a Rigid Body
163(1)
12.7 Moments of Inertia
164(1)
12.8 Equations of Motion for a Rotor
165(1)
12.9 Explicit Solutions
165(2)
12.10 Loss of Orthogonality
167(1)
12.11 Implicit Method
168(2)
12.12 Example: Free Symmetric Rotor
170(1)
12.13 Kinetic Energy of a Rotor
171(1)
12.14 Parametrization by Euler Angles
172(1)
12.15 Cayley-Klein parameters, Quaternions, Euler Parameters
172(4)
12.16 Solving the Equations of Motion with Quaternions
176(3)
Problems
176(3)
13 Simulation of Thermodynamic Systems
179(14)
13.1 Force Fields for Molecular Dynamics Simulations
179(2)
13.1.1 Intramolecular Forces
179(1)
13.1.2 Intermolecular Forces
180(1)
13.1.3 Approximate Separation of Rotation and Vibrations
180(1)
13.2 Simulation of a van der Waals System
181(5)
13.2.1 Integration of the Equations of Motion
181(1)
13.2.2 Boundary Conditions and Average Pressure
182(1)
13.2.3 Initial Conditions and Average Temperature
183(1)
13.2.4 Analysis of the Results
183(3)
13.3 Monte Carlo Simulation
186(7)
13.3.1 One-Dimensional Ising Model
186(2)
13.3.2 Two-Dimensional Ising Model
188(1)
Problems
189(4)
14 Random Walk and Brownian Motion
193(14)
14.1 Random Walk in One Dimension
194(2)
14.1.1 Random Walk with Constant Step Size
195(1)
14.2 The Freely Jointed Chain
196(6)
14.2.1 Basic Statistic Properties
197(2)
14.2.2 Gyration Tensor
199(1)
14.2.3 Hookean Spring Model
200(2)
14.3 Langevin Dynamics
202(5)
Problems
204(3)
15 Electrostatics
207(22)
15.1 Poisson Equation
207(8)
15.1.1 Homogeneous Dielectric Medium
207(2)
15.1.2 Charged Sphere
209(1)
15.1.3 Variable ε
210(1)
15.1.4 Discontinous ε
211(1)
15.1.5 Solvation Energy of a Charged Sphere
211(2)
15.1.6 The Shifted Grid Method
213(2)
15.2 Poisson Boltzmann Equation for an Electrolyte
215(1)
15.2.1 Discretization of the Linearized Poisson-Boltzmann Equation
216(1)
15.3 Boundary Element Method for the Poisson Equation
216(6)
15.3.1 Integral Equations for the Potential
217(2)
15.3.2 Calculation of the Boundary Potential
219(3)
15.4 Boundary Element Method for the Linearized Poisson-Boltzmann Equation
222(1)
15.5 Electrostatic Interaction Energy (Onsager Model)
223(6)
15.5.1 Example: Point Charge in a Spherical Cavity
225(1)
Problems
225(4)
16 Waves
229(14)
16.1 One-Dimensional Waves
229(2)
16.2 Discretization of the Wave Equation
231(1)
16.3 Boundary Values
232(1)
16.4 The Wave Equation as an Eigenvalue Problem
233(4)
16.4.1 Eigenfunction Expansion
233(1)
16.4.2 Application to the Discrete One-Dimensional Wave Equation
234(3)
16.5 Numerical Integration of the Wave Equation
237(6)
16.5.1 Simple Algorithm
237(1)
16.5.2 Stability Analysis
238(2)
16.5.3 Alternative Algorithm with Explicit Velocities
240(1)
16.5.4 Stability Analysis
240(2)
Problems
242(1)
17 Diffusion
243(10)
17.1 Basic Physics of Diffusion
243(1)
17.2 Boundary Conditions
244(1)
17.3 Numerical Integration of the Diffusion Equation
245(8)
17.3.1 Forward Euler or Explicit Richardson Method
245(1)
17.3.2 Stability Analysis
245(2)
17.3.3 Implicit Backward Euler Algorithm
247(1)
17.3.4 Crank-Nicolson Method
248(1)
17.3.5 Error Order Analysis
249(1)
17.3.6 Practical Considerations
250(1)
17.3.7 Split Operator Method for d > 1 Dimensions
250(2)
Problems
252(1)
18 Nonlinear Systems
253(24)
18.1 Iterated Functions
253(7)
18.1.1 Fixed Points and Stability
254(2)
18.1.2 The Ljapunow Exponent
256(1)
18.1.3 The Logistic Map
257(1)
18.1.4 Fixed Points of the Logistic Map
258(1)
18.1.5 Bifurcation Diagram
259(1)
18.2 Population Dynamics
260(2)
18.2.1 Equilibria and Stability
260(2)
18.2.2 The Continuous Logistic Model
262(1)
18.3 Lotka-Volterra model
262(3)
18.3.1 Stability Analysis
263(2)
18.4 Functional Response
265(4)
18.4.1 Holling-Tanner Model
266(3)
18.5 Reaction-Diffusion Systems
269(8)
18.5.1 General Properties of Reaction-Diffusion Systems
269(1)
18.5.2 Chemical Reactions
270(1)
18.5.3 Diffusive Population Dynamics
270(1)
18.5.4 Stability Analysis
270(2)
18.5.5 Lotka-Volterra Model with Diffusion
272(1)
Problems
273(4)
19 Simple Quantum Systems
277(32)
19.1 Quantum Particle in a Potential Well
278(4)
19.2 Expansion in a Finite Basis
282(2)
19.3 Time-Independent Problems
284(8)
19.3.1 Simple Two-Level System
285(1)
19.3.2 Three-State Model (Superexchange)
286(4)
19.3.3 Ladder Model for Exponential Decay
290(2)
19.4 Time-Dependent Models
292(5)
19.4.1 Landau-Zener Model
293(1)
19.4.2 Two-State System with Time-Dependent Perturbation
293(4)
19.5 Description of a Two-State System with the Density Matrix Formalism
297(12)
19.5.1 Density Matrix Formalism
297(3)
19.5.2 Analogy to Nuclear MagneticResonance
300(2)
19.5.3 Relaxation Processes---Bloch Equations
302(5)
Problems
307(2)
Appendix 309(2)
References 311(4)
Index 315
1984 PhD in experimental and theoretical physics 1996 Habilitation in theoretical physics since 1999 lecturer at Technische Universitat Munchen (TUM) 2001 and 2003, visiting scientist at AIST, Tsukuba,Japan 2006-2008 temporary leader of the Institute for Theoretical Biomolecular Physics (T38) at TUM