SCHRODINGER TOOLBOX Version of April 1999 ==========================================================================schrodingeris a toolbox of MATLAB files which which gives the neophyte student of Quantum Mechanics an interactive access to some of the basic methods of solving the Schrodinger equation. Read more in thereadme.txtfile and in the M-files listed below! The files can be run on any computer with the MATLAB program installed with a graphical interface. They have been tested with MATLAB 5.2 on a PowerMac 7600 and on a PC/Linux. They should run also on version 4.2. The speed evidently depends on the platform, but it can be adapted to your computer through the choice of the number of lattice points and basis functions. This choice will inevitably also influence the accuracy of the solutions. Start the session by executing the filestart.mthen making choices by clicking the buttons and inserting values in editing windows. You may have to change your window size and the font size in some places! ========================================================================== Files in the schrodinger folder, F - says it is a function file. ========================================================================== Contents.m - this file Readme.txt - Read this file for an introduction. start.m - EXECUTE THIS FILE TO GET STARTED ========================================================================== DEMOS - you can execute these independently of========================================================================== angl.m - plots the angular dependence of spherical harmonics. barrier.m - finds the transmission coeff for a 'square' barrier/hole. besjexp.m - finds expansions in Bessel functions J_m bound1d.m - finds bound states for 1D Schrodinger particle bound3d.m - finds bound states for central potential defined in boundst.m - menu file for bound state problems choice.m - utility for interactive choice of potential from diffrac.m - calculates the diffraction from an array of slits evolut.m - displays the evolution of a wave packet using iteration. hard.m - displays scattering cross sections for hard sphere in 3D. hatom.m - menu displaying some features of hydrogen eigenstates. inbox.m - menu file for particle in a box + potential kp.m - finds spectrum of Kronig-Penney like model. legexp.m - expansions in Legendre polynomials and functions. integrat.m - shows effect of instability on numerical integration matrix1.m - solves for eigenvalues/functions using matrix approx. matrix2.m - solves for eigenvalues only, faster - uses slider input. morse.m - calculates the eigenvalues of Morse potential orbitals.m - graphic display of H orbitals. per1d.m - menu choice of periodic potential problems pw2d - scattering for 2D circular potential well pw3d.m - partial wave method in 3Dscattering qho.m - displays some properties of QHO eigenstates. restun.m - finds narrow tunneling resonances. scatt.m - a menu for 1D scattering problems. scatt3d.m - menu for 3D scattering problems. schr1.m - interactive search for eigenvalues/functions. schr2.m - interactive search for bound states in 1D. schr3.m - automatic search for bound states in 1D. special.m - a menu for some special functions. stepp.m - scattering on a step potential plus an additional term. trans1.m - transmission for a multiple barrier trans2.m - transmission for a biased multiple barrier trans3.m - transmission for a multiple barrier with random heights transm.m - transmission coefficient and Bloch spectrum in 1D. trix.m - calculates Bloch solutions in a discrete model tunnel.m - scattering and tunneling of wave packet in 1D. wavepac.m - menu file for wave packet evolutions well.m - partial wave scattering for potential well. well1.m - bound states in various 1D quantum wells. well2.m - bound state energies in quadratic and circular 2D wells well3.m - eigenvalues of an infinite quadratic or circular 2D well well4.m - eigenvalues of infinite rectangular 2D well wellbd.m - bound states in a spherical 'square' well. ========================================================================== FUNCTION FILES ========================================================================== aias.m - F - asymptotics for Airy functions for positive arguments. besjz.m - F - calculates zeros of Bessel functions J_m binom.m - F - calculates binomial coefficients crop.m - F - utility which crops values outside a finite range. evalpol.m - F - polynomial evaluation fact.m - F - factorial for integer-valued matrix inputs. fgh - F - Calculates Schrodinger eigenvalues/states using the Fourier Grid Hamiltonian method findzero.m - F - finds zeros by spline interpolation. fresn.m - F - calculates the complex Fresnel function gegenb.m - F - calculates coefficients of Gegenbauer polys glue.m - F - glues jumps of given amplitude in a function ho.m - F - evaluates QHO eigenfunctions. hp.m - F - calculates coefficients of Hermite polynomials. hydrogen.m - F - calculates hydrogen eigenstate amplitudes. inv4.m - F - inversion for 2x2 matrices represented as 4-vectors jacobi.m - F - calculates coefficients of Jacobi polynomials lagp.m - F - coefficients of Laguerre polynomials laguerre.m - F - evaluates Laguerre polynomials, matrix arguments legf.m - F - calculates Legendre functions for a matrix argument legfun.m - F - calculates a set of Legendre functions legpol.m - F - calculates the values of a set of Legendre polys mad.m - F - adds a row vector to a matrix, adjusting the dimensions mult4.m - F - multiplication of 2x2 matrices represented as 4-vectors numerov1.m - F - integrates Schrodinger eq, keeps boundary values only numerov2.m - F - integrates Schrodinger eq, keeps solution numerov3.m - F - variant of numerov1, use when memory gets short pot1.m - F - list of potentials used by radial.m - F - calculates hydrogen radial eigenfunctions radnl.m - F - another calculation of radial solutions sde.m - F - defines a Schrodinger 1D DE for ode45 etc. transfer.m - F - calculates transfer matrix using Numerov integration. trf1.m - F - transfer matrix for an interval, constant potential trf2.m - F - transfer matrix for an interval, linear potential wkb.m - F - calculates semiclassical WKB eigenvalues yl.m - F - calculates spherical harmonics ylm.m - F - - " -, other format only. zed.m - F - an auxiliary function used to find zeros of Bessels zeroai.m - F - calculates zeros of Airy function ========================================================================== GRAPHICS - INPUTS - TEXT ========================================================================== edit1.m - F - input through editing a string cbutt.m - F - a green 'continue' button bbutt.m - F - blue button gbutt.m - F - green button obutt.m - F - grey non-functional button rbutt.m - F - red button slider1.m - F - input using a slider suptitle.m - F - useful graphics (by Drea Thomas) text0.m - F - default text box, 12 pt wbutt.m - F - a red 'wait' button ========================================================================== © Goran Lindblad 1999 - gli@theophys.kth.se