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slgcd.py
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#!/usr/bin/python3
# _*_ coding: utf-8 _*_
import os
import im2gif
import cmath as cm
import numpy as np
from io import BytesIO
from PIL import Image as im
from matplotlib import pyplot as plt
# set barrier width a
a = 0.16
# set ratio of E/U0
ratio = float(input('please input ratio of E/U0: '))
# to avoid ratio being smaller than 0.01 or equal to 1
ratio = 0.01 if ratio < 0.01 else ratio if ratio != 1 else ratio + 1e-10
# set barrier constant k0
k0 = 5
# set scale value.
scale = 4 / cm.sqrt(ratio)
# define wave vactor k
k1 = scale * k0 * cm.sqrt(ratio) # wave vector of part 1 and 3
k2 = scale * k0 * cm.sqrt(ratio - 1) # wave vector of part 2
# define intensity ratio of wave
# A and A_ belong to wave of part 1
# B and B_ belong to wave of part 2
# C and C_ belong to wave of part 3
# De is just a common denominator value
# we define A = 1 and others will be directly proportional to A
A = 1.2
De = pow(k1 - k2, 2) * np.exp(1j * k2 * a) - pow(k1 + k2, 2) * np.exp(-1j * k2 * a)
A_ = 2j * (pow(k1, 2) - pow(k2, 2)) * np.sin(a * k2) * A / De
C = -4 * k1 * k2 * np.exp(-1j * k1 * a) * A / De
B = (A * k1 + A * k2 - A_ * k1 + A_ * k2) / (2 * k2)
B_ = (A * k2 - A * k1 + A_ * k1 + A_ * k2)/ (2 * k2)
# define three part
x1 = np.linspace(-1, 0, 10e3) # x limit of part 1
x2 = np.linspace(0, a, 10e3) # x limit of part 2
x3 = np.linspace(a, a + 1, 10e3) # x limit of part 3
# define wave function
y1_r = A * np.exp(1j * k1 * x1) # right wave function of part 1
y1_l = A_ * np.exp(-1j * k1 * x1) # left wave function of part 1
y2_r = B * np.exp(1j * k2 * x2) # right wave function of part 2
y2_l = B_ * np.exp(-1j * k2 * x2) # left wave function of part 2
y3_r = C * np.exp(1j * k1 * x3) # right wave function of part 3
y1 = y1_r + y1_l # wave function of part 1
y2 = y2_r + y2_l # wave function of part 2
y3 = y3_r # wave function of part 3
# create a new figure
plt.figure(figsize=(10,45/8))
# set axis scope
plt.axis([-1, a + 1, -4, 4])
# hide the axis
plt.axis('off')
# set plot hold on
plt.hold(True)
# draw wave in part 1 and get three plot handle for data updating later
h10, = plt.plot(x1, np.real(y1), 'g-', label='composite wave', linewidth=2)
h11, = plt.plot(x1, np.real(y1_r), 'b--', label='incident wave', linewidth=2)
h12, = plt.plot(x1, np.real(y1_l), 'r--', label='reflected wave', linewidth=2)
# draw legend
plt.legend(fontsize=14, frameon=True, fancybox=True, framealpha=0.3)
# draw wave in part 2 and get three plot handle for data updating later
h20, = plt.plot(x2, np.real(y2), 'g-', linewidth=2)
h21, = plt.plot(x2, np.real(y2_r), 'b--', linewidth=2)
h22, = plt.plot(x2, np.real(y2_l), 'r--', linewidth=2)
# draw wave in part 3
h30, = plt.plot(x3, np.real(y3), 'g-', linewidth=2)
# draw barrier line
plt.plot([-1,0,0,a,a,a+1], [-3,-3,3,3,-3,-3], 'k-', linewidth=2)
# draw reference center line
plt.plot([-1, a + 1], [0, 0], color='gray', linestyle='-.')
# set plot hold off
plt.hold(False)
# draw text information
## define font dict creater function
def font(family='serif', color='black', weight='normal', size='16'):
return {'family': family, 'color': color, 'weight': weight, 'size': size}
## draw title
plt.title('Barrier Penetration And Tunneling', fontdict=font(size=20))
## draw barrier height value U0
plt.text(a, 3, '$U_0$', fontdict=font(size=20))
## draw value of E/U0
plt.text(-.8, 3, '$\itE/\itU_0=\it%.2f$' % ratio, fontdict=font(size=20))
## draw barrier left limit
plt.text(-.02, -3.3, '$0$', fontdict=font())
## draw barrier right limit
plt.text(a-.02, -3.3, '$a$', fontdict=font())
## draw x axis mark 'x'
plt.text(a+.95, -2.95, '$x$', fontdict=font())
## draw water mark of author
plt.text(a+.7, -3.4, '$author: ph$', fontdict=font(color='gray'))
# show plot
# if you want to get dynamic plot, just annotate this.
plt.show()
#create dynamic plot
# set gif save dir
gif_root = './gif'
# check gif root dir
if not os.path.isdir(gif_root):
os.makedirs(gif_root)
# set frame number N
FN = 40
# pre storage allocation
images = []
for i in range(FN):
# add time factor
Et = np.exp(-2j * np.pi * i / FN)
# update the plot data
h10.set_ydata(np.real(y1 * Et))
h11.set_ydata(np.real(y1_r * Et))
h12.set_ydata(np.real(y1_l * Et))
h20.set_ydata(np.real(y2 * Et))
h21.set_ydata(np.real(y2_r * Et))
h22.set_ydata(np.real(y2_l * Et))
h30.set_ydata(np.real(y3 * Et))
# create bytes buffer
buf = BytesIO()
# save plot date to buf
plt.savefig(buf, format='png')
# read buf as image date and append to images
images.append(im.open(buf))
# set gif file save path
gif_path = os.path.join(gif_root, 'slgc_%.2f.gif' % ratio)
# create GIF dynamic plot from images
im2gif.writeGif(filename=gif_path, images=images, duration=2 / FN)
# print status message
print('gif file created at path: %s.' % os.path.abspath(gif_path))