Computational Physics using Maple

A package of Maple worksheets to accompany a physics undergraduate curriculum. This is work in progress, if you like to send feedback: marko@yorku.ca is the right address (a CD can be obtained for a \$10 handling charge). The links at the chapter number connect to HTML pages, the links on the right allow to download the worksheet. Most of the worksheets can be used with Maple V Release 5, all of them should run under maple6 through maple8. This work was supported by York University and by the Natural Sciences and Engineering Research Council of Canada, and most recently (2003) under the Maplesoft course adoption program. To get the Maple software itself, go to www.maplesoft.com

April 2005 edition written by Marko Horbatsch

The first *.mws link is to the complete worksheet with output, the second is to the *.mws code with text which is typically 20-40 kB in size.

For some worksheets lecture notes exist in the form of jpg-files, these are linked as N_i

1. Introduction to Maple

1.1 Crash course for physicists Intro.mws Intro.mws

1.2 Integration in Maple: branch cuts problems IntBug.mws

1.3 Energy and momentum conservation Bullet.mws Bullet.mws

1.4 Rocket thrust: momentum conservation with variable mass Rocket.mws Rocket.mws

1.5 Firing a cannonball: solution to Newton's equation Cannon.mws Cannon.mws ; N_1;N_2

1.6 Compton scattering Compton.mws Compton.mws

1.7 Moment of Inertia of an Ellipsoid: Eigenvectors in LinearAlgebra MomentInertia.mws MomentInertia.mws

2. Classical Mechanics

2.1 Harmonic oscillator: the mass-spring system HOmovie.mws HOmovie.mws; N_1;N_2;N_3

2.2 Coupled oscillators CoupledHO.mws CoupledHO.mws; N_1

2.3 Mathematical pendulum Pendulum.mws Pendulum.mws; N_1;N_2

2.4 Work and force Work.mws Work.mws

2.5 Work Integral for a force field with curl WorkIntegral.mws WorkIntegral.mws

2.6 Kepler Problem Kepler.mws Kepler.mws

2.7 Foucault Pendulum Foucault.mws Foucault.mws

2.8 Pulling Yo-Yo's on a table: all about friction PulledRoll.mws PulledRoll.mws

2.9 Euler's equation: the spinning textbook Euler.mws Euler.mws

2.10 The free gyroscope from Euler's equationsFreeGyro.mws FreeGyro.mws; N_1;N_2;N_3.

2.11 The precessing and nutating gyroscope Gyro.mws Gyro.mws

2.12 The Tippy-top or tippe top TippyTop.mws TippyTop.mws;N_1; N_2;N_3; N_4;N_5; avi-movie;virtual reality mpg-movie by C. Friedl and A.Wobst; Link

2.13 Vibrating wine glass Glass.mws Glass.mws

2.14 Plucking a string: The 1-dim wave equation: WaveEqn.mws WaveEqn.mws; N_1

2.15 Differential cross section: Screened Rutherford potential ClassicalScattering.mws ClassicalScattering.mws;

3. Electricity and Magnetism

3.1 Gauss' law Gauss.mws Gauss.mws

3.2 Electric field lines and charged particle trajectories Fieldline.mws Fieldline.mws

3.3 Ampere's law: magnetic field from an electric current Ampere.mws Ampere.mws

3.4 Biot-Savart law BiotSavart.mws BiotSavart.mws

3.5 Magnetic field lines: the current loop Currentloop.mws Currentloop.mws

3.6 Magnetic bottle MagBottle.mws MagBottle.mws

3.7 Electric field between concentric cylinders: Laplace equation Laplace.mws Laplace.mws

3.8 Lorentz Force: electrons in a combined electric and magnetic field LorentzForce.mws LorentzForce.mws

3.9 Electric field of a charge cloud between concentric cylinders: Poisson equation Poisson.mws Poisson.mws

4. Electronics

4.1 RLC circuits RLCcircuit.mws RLCcircuit.mws

4.2 Signal generation by an RC circuit SignalGen.mws SignalGen.mws

4.3 Fourier transform: continuous and discrete (FFT) FFT.mws FFT.mws; N_1, N_2

5. Special Relativity and Modern Physics

5.1 Time dilation and length contraction: the Lorentz transformation SpecialRel.mws SpecialRel.mws

5.2 Relativistic dynamics: conservation laws for energy and momentum RelDynamics.mws RelDynamics.mws

5.3 Schroedinger wave equation: a differential equation - eigenvalue problem Schroedinger.mws Schroedinger.mws

5.4 Fourier Series: solve ordinary differential equations with linear algebra techniques. FourierSeries.mws FourierSeries.mws

5.5 Wavepackets: from simple superposition of plane waves to a Gaussian WP Wavepacket.mws Wavepacket.mws

5.6 Tunneling through potential barriers: transmission resonances Tunnel.mws Tunnel.mws; N_1

5.7 The matrix representation of quantum mechanics MatrixRep.mws MatrixRep.mws; N_1;N_2;

5.8 Ehrenfest's theorems: from quantum to classical mechanics Ehrenfest.mws Ehrenfest.mws

5.9 Uncertainty relation for angular momentum Uncertainty.mws Uncertainty.mws

5.10 Atomic structure of helium in the central field approximation AtomicModel.mws AtomicModel.mws

5.11 Angular momentum coupling: Clebsch-Gordan coefficients Clebsch.mws Clebsch.mws

5.12 Perturbation Theory: a semi-convergent series Perturbation.mws Perturbation.mws

5.13 Scattering from a spherical potential well: differential cross section PhaseShift.mws PhaseShift.mws

5.14 Non-commutative operator product and Taylor expansion of operators NoncomProduct.mws NoncomProduct.mws

5.15 Quantum phase space distribution: Wigner function Wigner.mws Wigner.mws

5.16 Numerically calculated Wigner function for wavepacket scattering WignerDiscrete.mws WignerDiscrete.mws

5.17 The mapped Fourier grid method in quantum mechanics MappedFourierGrid.mws MappedFourierGrid.mws; N_1;N_2;N_3;

5.18 Josephson Junction: tunneling of Cooper pairs Josephson.mws Josephson.mws

5.19 Introduction to quantum logic gates Qubit.mws Qubit.mws

5.20 Multidimensional Fourier Transform (Maple9 and up) MultidFFT.mws MultidFFT.mws

5.21 Quantum Pendulum QuantumPendulum.mws QuantumPendulum.mws

5.22 Periodic N-site Lattice: Bloch States BlochStates.mws BlochStates.mws

6. Optics

6.1 Fraunhofer diffraction using Feynman's sum over paths method FraunhoferFeynman.mws FraunhoferFeynman.mws

6.2 Diffraction Patterns from Multi-Slit Apertures FourierOptics.mws FourierOptics.mws

7. Thermodynamics and Thermostatistics

7.1 Ideal gas simulation IdealGas.mws IdealGas.mws

7.2 Entropy and Temperature Entropy.mws Entropy.mws

7.3 Heat Equation in 1 dimension HeatEqn.mws HeatEqn.mws; N_1;N_2;N_3 ;N_4

7.4 Evaporative cooling in an ergodic system Cooling.mws Cooling.mws

8. Nonlinear Physics: Chaos

8.1 Double pendulum DblPendulum.mws DblPendulum.mws

8.2 Duffing oscillator Duffing.mws Duffing.mws

8.3 Measuring fractal dimensions: Koch curve and Duffing attractor FractalDimension.mws FractalDimension.mws;N_1

9. Experimental Physics

9.1 Experimental uncertainty: the normal (Gaussian) distribution ExpUncertainty.mws ExpUncertainty.mws

9.2 Linear least squares fit to experimental data DataAnalysis.mws DataAnalysis.mws

9.3 Exponential curve fit: charging and discharging a capacitor ExpFit.mws ExpFit.mws

9.4 Fitting a quadratic function to noisy data NoisyData.mws NoisyData.mws

9.5 Nuclear decays: a test case for Poisson statistics Decay.mws Decay.mws