Computational Physics

1.2 Classical mechanics and statistical mechanics 3 x t 2 0 1 –2.5 –2 –1.5 –1 –0.5 0.5 1.5 2.5 0 102030405060708090100 Figure 1. ...

4 Introduction 1.3 Stochastic simulations In the previous section we have explained how numerical algorithms for solving Newton’ ...

1.4 Electrodynamics and hydrodynamics 5 one of its neighbour sites, which is chosen at random (there are four neighbours for eac ...

6 Introduction 1.5 Quantum mechanics In quantum mechanics we regularly need to solve the Schrödinger equation for one or more pa ...

1.6 Relations between quantum mechanics and classical statistical physics 7 standard numerical methods for solving partial diffe ...

8 Introduction and that of a quantum system with quantum HamiltonianH: ZQM=Tr(e−H/(kBT)); (1.4) ‘Tr’ denotes the trace of the op ...

1.9 About this book 9 to include some damping mechanism in the equations of motion and then let the nuclei relax to their ground ...

10 Introduction illustration of solving a rather simple (not completely trivial) physical problem on a computer. The results of ...

Exercises 11 Perhaps the most decisive criterion for choosing a particular language is whether you have experience with it. Ther ...

12 Introduction p x –2.5 –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 2.5 3 –2.5 –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 Figure 1.3. Strange attractor fo ...

References 13 to a straight line. The slope of this line is then the fractal dimension which must be about 1.7. References [1] J ...

2 Quantum scattering with a spherically symmetric potential 2.1 Introduction In this chapter, we shall discuss quantum scatterin ...

2.1 Introduction 15 dΩ θ φ y x z Figure 2.1. Geometry of a scattering process. There might be many different motives for obtaini ...

16 Quantum scattering with a spherically symmetric potential This is a partial differential equation in three dimensions, which ...

2.1 Introduction 17 V r V= 10 V= 0 V= 205 Figure 2.2. The radial wave functions forl=0 for various square well potential depth ...

18 Quantum scattering with a spherically symmetric potential with an angular momentum smaller than
lmax=
krmaxwill ‘feel’ the po ...

2.2 A program for calculating cross sections 19 calculate differential cross sections, we need Legendre polynomials too. In Appe ...

20 Quantum scattering with a spherically symmetric potential bothr 1 andr 2 are equal to an integer times the integration steph( ...

2.2 A program for calculating cross sections 21 We shall now turn to the H–Kr interaction. The two-atom interaction potential fo ...

22 Quantum scattering with a spherically symmetric potential 2.2.2 The spherical Bessel functions For the present problem, you n ...