Demonstrations Using RLaB

• packet_demo.r: This computes and displays the evolution of a free particle wave packet. The dispersion relation may be easily changed to show how phase and group velocities vary depending on the dispersion relation.
• propagator.r: This computes the one dimensional propagator for the development of wave packets at a specified time. There is a choice of three dispersion relations.
• symmwell.r: This plots a function, the zeros of which give the allowed energies for symmetric solutions to the finite square well problem.
• shoot_demo.r: This solves the the time-independent Schrodinger equation for the case of a massive particle bound by a potential well using the so-called shooting method. The integration is carried out from left to right across the potential. The user makes successive guesses for the energy until the right-hand boundary condition is satisfied.
• scatter1_demo.r: Displays the absolute square of the wavefunction for one-dimensional scattering from an isolated potential. The potential and the total energy are also shown. The theory of one-dimensional scattering is used in the development of this demonstration. doscatter.r calls scatter1_demo.r repeatedly for a range of energies and plots the reflection and transmission fractions.
• qcalc.r: This computes the matrix used to make finite forward and inverse Fourier transforms.
• ho_demo.r: This computes the harmonic oscillator eigenfunctions and eigenvalues using the finite matrix approximation to the Hamiltonian.
• anho_demo.r: This computes the eigenfunctions and eigenvalues using the finite matrix approximation for an anharmonic oscillator with a scaled potential energy function of the form U(x) = x^2/2 + epsilon*exp(-x^2).
• p10.r: This computes the eigenfunctions and eigenvalues using the finite matrix approximation for a scaled one-dimensional potential well of the form U(x) = x^10.
• solid.r: This program computes the eigenvalues and eigenvectors for a periodic potential. It demonstrates some of the effects seen in a crystalline solid.
• evolve_demo.r: This computes the time evolution of a wave packet in a potential. It uses the output of some eigenvector/eigenvalue calculator like ho_demo.r or anho_demo.r as a source of the necessary information.
• dwell_demo.r: This computes the eigenvectors and eigenvalues using the finite matrix approximation for a potential consisting of two equal gaussian wells with controllable separation. adwell_demo.r does the same for two unequal gaussian wells.
• dipole_demo.r: This computes the dipole moment between initial and final state vectors for one-dimensional bound states. Obtain the state vectors from ho_demo.r or anho_demo.r. The ideas behind this subject are developed in the section on time dependent perturbation theory.
• forcing_demo.r: This demonstration computes the time-dependent behavior of the bound states of an attractive potential when it is perturbed by a force periodic in time but constant in space. See time dependent perturbation theory.
• ho2energies.r: This lists the energies and the state numbers for the two-dimensional harmonic oscillator in order of increasing energy.
• xydipole.r: This computes the dipole moment matrix elements for the two-dimensional harmonic oscillator.
• ho2perturb.r: This computes the perturbation energies for a two-dimensional harmonic oscillator with lambda = 1, perturbed by the potential U(x,y) = -0.2*exp(-x^2 - y^2).
• ident.r: This plots the joint probability distribution for two particles in different energy states in an infinite square well. Three cases are shown: 1) two non-identical particles; 2) two identical Fermions; 3) two identical Bosons.