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#!/usr/bin/env python3

# NOTE:
# - Write superpositions of wavefunction into a
#   plotting script
# - The wavefunction is a linear combination according to
#    psi(x) = sum[ (1/N)*cos(k*pi*x), k=1..N]

import os  

# The primitive wavefunction
def wave(N, k): 
    return '1/{0}.0*cos({1}.0*pi*x)'.format(N,k)

# Superimposing the wavefunction
def loop(L):
    function = ''
    for i in range(1, L+1):
        if i < L:
            function += wave(L, i) + '+' 
        else:
            function += wave(L, i)
    return '(' + function + ')*(' + function + ')', L

# Generating the GNUPlot script
def writeGnuString(functions, lw='2'): 
    gs  = ''
    gs += 'set xrange[-1:1]\n'
    gs += 'plot \\' + '\n'
    i = 0 
    for func in functions: 
        if i < len(functions)-1:
            gs += '{0} title "N={1}" lw {2}, \\'\
                    .format(func[0], func[1], lw) + '\n'
            i+=1
        else:
            gs += '{0} title "N={1}" lw {2};\n'\
                    .format(func[0], func[1], lw) 
    gs += 'pause -1;'
    return gs

# Work
functions = []

# Number of superpositions
for i in [2,5,10,25]:
    functions.append(loop(i))

file = open('wave.gnu', 'w')
file.write(writeGnuString(functions))
file.close()

os.system('gnuplot wave.gnu')

Code: Alles auswählen

def loop(L):
    """Superimposing the wavefunction"""
    function = '+'.join(wave(L, i) for i in range(1, L + 1))
    return '({0})*({0})'.format(function), L

Code: Alles auswählen

def wave(N, k):
    """The primitive wavefunction"""
    return '1/%s.0*cos(%s.0*pi*x)' % (N, k)


def loop(L):
    """Superimposing the wavefunction"""
    function = '+'.join(wave(L, i) for i in range(1, L + 1))
    return '(%s)*(%s)' % (function, function), L