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Theoretical Physics on the Personal Computer

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概要 This book is based on the lecture course "Computer applications in Theo retical Physics", which has been offered at the University of Tiibingen since 1979. This course had as its original aim the prep...aration of students for a nu merical diploma course in theoretical physics. It soon became clear, however, that the course provides a valuable supplement to the fundamental lectures in theoretical physics. Whereas teaching in this field had previously been prin cipally characterised by the derivation of equations, it is now possible to give deeper understanding by means of application examples. A graphical presen tation of numerical results proves to be important in emphasizing the physics. Interaction with the machine is also valuable. At the end of each calculation the computer should ask the question: "Repeat the calculation with new data (yes/no )?". The student can then answer "yes" and input the new data, e.g. new starting values for position and velocity in solving an equation of motion. The programming of a user-friendly dialogue is not really difficult, but time consuming. At the beginning of the course the student therefore constructs only the numerical parts of the programs. The numerical parts are therefore deleted from the programs under consideration, and newly programmed by the student. Later on, the programming of the graphical output and of the dialogue is taught.続きを見る
目次 1. Introduction
1.1 Programming of the Numerical Portions of the Programs
1.2 Programming of the Input and Output
2. Numerical Differentiation and Introduction into Screen Dialogue
2.1 Formulation of the Problem
2.2 Mathematical Methods
2.3 Programming
2.4 Exercises
2.5 Solutions to the Exercises
3. Numerical Integration
3.1 Formulation of the Problem
3.2 Numerical Methods
3.3 Programming
3.4 Exercises
3.5 Solutions to the Exercises
4. Harmonic Oscillations with Sliding and Static Friction, Graphical Output of Curves
4.1 Formulation of the Problem
4.2 Numerical Treatment
4.3 Programming
4.4 Exercises
4.5 Solutions to the Exercises
5. Anharmonic Free and Forced Oscillations
5.1 Formulation of the Problem
5.2 Numerical Treatment
5.3 Programming
5.4 Exercises
5.5 Solutions to the Exercises
6. Coupled Harmonic Oscillations
6.1 Formulation of the Problem
6.2 Numerical Method
6.3 Programming
6.4 Exercises
6.5 Solutions to the Exercises
7. The Flight Path of a Space Craft as a Solution of the Hamilton Equations
7.1 Formulation of the Problem
7.2 Mathematical Methods
7.3 Programming
7.4 Exercises
7.5 Solutions to the Exercises
8. The Celestial Mechanics Three-body Problem
8.1 Formulation of the Problem
8.2 Mathematical Method
8.3 Programming
8.4 Exercises
8.5 Solutions to the Exercises
9. Computation of Electric Fields by the Method of Successive Over-relaxation
9.1 Formulation of the Problem
9.2 Numerical Method
9.3 Programming
9.4 Exercises
9.5 Solutions to the Exercises
10. The Van der Waals Equation
10.1 Formulation of the Problem
10.2 Numerical Method
10.3 Programming
10.4 Exercises
10.5 Solutions to the Exercises
11. Solution of the Fourier Heat Conduction Equation and the 'Geo-Power Station'
11.1 Formulation of the Problem
11.2 Method of Solution
11.3 Programming
11.4 Exercises
11.5 Solutions to the Exercises
12. Group and Phase Velocity in the Example of Water Waves
12.1 Formulation of the Problem
12.2 Numerical Method
12.3 Programming
12.4 Exercises
12.5 Solutions to the Exercises
13. Solution of the Radial Schrödinger Equation by the Fox-Goodwin Method
13.1 Formulation of the Problem
13.2 Numerical Method of Solution
13.3 Programming
13.4 Exercises
13.5 Solutions to the Exercises
14. The Quantum Mechanical Harmonic Oscillator
14.1 Formulation of the Problem
14.2 Numerical Method
14.3 Programming
14.4 Exercises
14.5 Solutions to the Exercises
15. Solution of the Schrödinger Equation in Harmonic Oscillator Representation
15.1 Formulation of the Problem
15.2 Numerical Method
15.3 Programming
15.4 Exercises
15.5 Solutions to the Exercises
16. The Ground State of the Helium Atom by the Hylleraas Method
16.1 Formulation of the Problem
16.2 Setting up the State Basis and the Matrix Equation
16.3 Programming
16.4 Exercises
16.5 Solutions to the Exercises
17. The Spherical Harmonics
17.1 Formulation of the Problem
17.2 Numerical Method
17.3 Programming
17.4 Exercises
17.5 Solutions to the Exercises
18. The Spherical Bessel Functions
18.1 Formulation of the Problem
18.2 Mathematical Method
18.3 Programming
18.4 Exercises
18.5 Solutions to the Exercises
19. Scattering of an Uncharged Particle from a Spherically Symmetric Potential
19.1 Formulation of the Problem
19.2 Mathematical Treatment of the Scattering Problem
19.3 Programming
19.4 Exercises
19.5 Solutions to the Exercises
References.
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登録日 2020.06.27
更新日 2020.06.28

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