SCHRODINGER TOOLBOX
Version of April 1999
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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.
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Contents.m - this file
Readme.txt - Read this file for an introduction.
start.m - EXECUTE THIS FILE TO GET STARTED
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DEMOS - you can execute these independently of
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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.
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FUNCTION FILES
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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
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GRAPHICS - INPUTS - TEXT
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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
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© Goran Lindblad 1999 - gli@theophys.kth.se
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