SCHRODINGER TOOLBOX
 Version of April 1999
==========================================================================
 schrodinger is 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 the
 readme.txt file 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 file start.m then 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!

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 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

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