Wave Packet Programming Lab

4 Sinusoid graph:

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from pylab import *

#Define constantsConstants

A=1 #Define the ampletude of the sin function

w=1 #sets the frequancey coefficient

#Calculation Loop: Note Nesting Carfully

for i in range(1,4):

    x = []

    sin_list = []

    for t in arange (-3.14, 3.14, 0.01):

        sine= A*sin(i*w*t)

        sin_list.append(sine)

        x.append(t)

    plot (x,sin_list)

show()

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50 sinusoid graph:

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from pylab import *

#Define constantsConstants

A=1 #Define the ampletude of the sin function

w=1 #sets the frequancey coefficient

#Calculation Loop: Note Nesting Carfully

for i in range(1,50):#every time the loop repeats this will change the harmonic

    x = [] # plots from -pi to +pi

    sin_list = [] #this includes the sine functions

    for t in arange (-3.14, 3.14, 0.01): # create tsh range of the graph and incriments

        sine= A*sin(i*w*t) #the function to be plotted

        sin_list.append(sine) # Adds the calculated vale from the sine function to the list appendex

        x.append(t)

    plot (x,sin_list)# plots values

show() #show the plot

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Localized particle

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from pylab import *

#Define constantsConstants

A=1 #Define the ampletude of the sin function

w=1 #sets the frequancey coefficient

Fourier_Series=[] #initialize the list of sine functions

#Calculate the harmonics of the sine functions

for i in range(1,300):#every time the loop repeats this will change the harmonic

    x = [] # plots from -pi to +pi

    sin_list = [] #this includes the sine functions

    for t in arange (-3.14, 3.14, 0.01): # create tsh range of the graph and incriments

        sine= A*sin(i*w*t) #the function to be plotted

        sin_list.append(sine) # Adds the calculated vale from the sine function to the list appendex

        x.append(t)

    #plot (x,sin_list)# plots values

    Fourier_Series.append(sin_list)

superposition = zeros(len(sin_list))

for function in Fourier_Series:

    for i in range(len(function)):

        superposition[i]+=function[i]

    

plot(x,superposition)

show()

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Envelope

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from pylab import *

#Define constantsConstants

A_list=[] #Define the amplitude of the sin function

w=1 #sets the frequancey coefficient

Fourier_Series=[] #initialize the list of sine functions

sigma = 1

coeff = 1

numberofharmonics=50

center = numberofharmonics/2

#Calculate the harmonics of the sine functions

for i in range(1,50):#every time the loop repeats this will change the harmonic

    x = [] # plots from -pi to +pi

    gauss = coeff*exp(-(i-center)**2/(2.*sigma**2))

    

    sin_list = [] #this includes the sine functions

    for t in arange (-3.14, 3.14, 0.01): # create tsh range of the graph and incriments

        sine= gauss*sin(i*w*t) #the function to be plotted

        sin_list.append(sine) # Adds the calculated vale from the sine function to the list appendex

        x.append(t)

    #plot(x,sin_list)# plots values

#show()

    Fourier_Series.append(sin_list)

superposition = zeros(len(sin_list))

for function in Fourier_Series:

    for i in range(len(function)):

        superposition[i]+=function[i]

plot(x,superposition)

show()

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Wave packet

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from pylab import *

#Define constantsConstants

w=1 #sets the frequancey coefficient

Fourier_Series=[] #initialize the list of sine functions

sigma = 10

coeff = 1

numberofharmonics=50

center = numberofharmonics/2

#Calculate the harmonics of the sine functions

for i in range(1,50):#every time the loop repeats this will change the harmonic

    x = [] # plots from -pi to +pi

    gauss = coeff*exp(-(i-center)**2/(2.*sigma**2))#Define the amplitude of the sin function

    sin_list = [] #this includes the sine functions

    for t in arange (-3.14, 3.14, 0.01): # create tsh range of the graph and incriments

        sine= gauss*sin(i*w*t) #the function to be plotted

        sin_list.append(sine) # Adds the calculated vale from the sine function to the list appendex

        x.append(t)

    #plot(x,sin_list)# plots values

#show()

    Fourier_Series.append(sin_list)

superposition = zeros(len(sin_list))

for function in Fourier_Series:

    for i in range(len(function)):

        superposition[i]+=function[i]

plot(x,superposition)

show()

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