Mathematica for Theoretical Physics: Electrodynamics, by Gerd Baumann

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By Gerd Baumann

This moment variation of Baumann's Mathematica in Theoretical Physics exhibits readers the right way to resolve actual difficulties and care for their underlying theoretical innovations whereas utilizing Mathematica to derive numeric and symbolic strategies. each one instance and calculation may be evaluated via the reader, and the reader can switch the instance calculations and undertake the given code to comparable or comparable difficulties. the second one version has been thoroughly revised and elevated into volumes: the 1st quantity covers classical mechanics and nonlinear dynamics. either themes are the foundation of a customary mechanics path. the second one quantity covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus.

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Extra info for Mathematica for Theoretical Physics: Electrodynamics, Quantum Mechanics, General Relativity and Fractals

Example text

4 Penning Trap The equations of motion for the X - and Y- components are coupled through the cross-product. The Z- component of the motion is completely decoupled from the X and Y coordinates. The last of these three equations è!!!! is equivalent to a harmonic oscillator with frequency 2 w0 . Thus, we immediately know the solution of the Z- coordinate given by è!!!! ZHtL = A cosI 2 w0 t + BM. 68) The arbitrary constants A and B are related to the initial conditions of the motion by ZHt = 0L = Z0 and Z ' Ht = 0L=Z0' .

91). 3, contains the necessary function PenningI[] to integrate Eqs. 91). Function PenningI[] also provides a graphical representations of the potential and the path of the relative particle. 11. Parameters l and n of this figure have been chosen so that the motion of the relative particle is regular. 12 shows a path for parameters l and n where chaotic motion is present. 11. -2 Relative motion in a Penning trap for l = 1 and n = 0. The plot of the particle is superimposed on the effective potential.

The plot of the particle is superimposed on the effective potential. The numerical integration extends over t œ @0, 100D. 0. 6, 0, cccccccccc , 100E; è!!!! 2 4 V 2 2 0 -2 2 0 z -1 -2 0 r 1 2 4. 5 Exercises 1. Create some pictures for a quadrupole arrangement of charges using the package PointCharge'. Choose the location of the charges in the representation plane of the potential section. What changes are required if your choice of coordinates for the charges is outside the representation plane?

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