def main(self, btn):
m = (9.11 * 10**(-31)) * float(self.Mass.text)
V = (1.602 * 10**(-19)) * float(self.Depth.text)
a = (10**(-10)) * float(self.hWidth.text)
R = quantumFn.radius(m, a, V)
x = 0
i = 1
j = 0
while R > i * np.pi:
i = i + 1
while R > (1 + 2 * j) * np.pi / 2:
j = j + 1
S = i + j
print(str(S) + " root(s) in total.")
#Initializes the "x" coord of the even and odd roots
evenRoot = np.zeros(i)
oddRoot = np.zeros(j)
#Used for indexing for the roots
ie = 0
jo = 0
#This is an interative root finder
#With an x0 used as an initial guess for the Newton function
dx = 0.0001 #This value has to be smaller to resolve bigger
x0 = 0.0000 #Scenarios!
#Used the Even/Odd root functions to establish a function
#With the radius as the parameter and "x" as a variable
ERoot = quantumFn.Evenroot(R)
ORoot = quantumFn.Oddroot(R)
#Since there will always be one root, this while loop
#Searches for the first even root, and then puts it into
#The evenRoot array
while np.absolute(ERoot(x0)) > 0.05: #This value has to
x0 = x0 + dx #Be small to resolve
print(x0) #Smaller scenarios!
print(R)
evenRoot[ie] = newton(ERoot, x0)
#If there is another even root, it will go into index 1
#For the even root array
#The next possible root will be when the radius is at least
#pi/2, so that is why x0 jumps to that value
ie = 1
x0 = (1 + 2 * jo) * np.pi / 2
#This loop will search for the remaining possible roots
#It goes in the order of looking for an odd root
#And then an even root.
while x0 < R:
while np.absolute(ORoot(x0)) > 0.05:
x0 = x0 + dx
oddRoot[jo] = newton(ORoot, x0)
jo = jo + 1
x0 = ie * np.pi #Resets the initial guess to next possible value
if x0 < R:
while np.absolute(ERoot(x0)) > 0.05:
x0 = x0 + dx
evenRoot[ie] = newton(ERoot, x0)
ie = ie + 1
x0 = (1 + 2 * jo) * np.pi / 2 #Resets again
#Initialize the propagation and tunneling vectors
#At this point I consolidate the even and odd roots
#Into single arrays instead of having arrays for
#Even and odd roots
propVector = np.zeros(S)
tunnVector = np.zeros(S)
ev = 0
od = 1
Roots = np.zeros(S)
#This is to define the vectors of each function
while ev < S:
Roots[ev] = evenRoot[int(ev / 2)]
ev = ev + 2
while od < S:
Roots[od] = oddRoot[int(od / 2)]
od = od + 2
print(Roots)
ev = 0
od = 1
while ev < S:
propVector[ev] = (10**(-10)) * Roots[ev] / a
tunnVector[ev] = (10**(-10)) * (quantumFn.radFunction(
Roots[ev], R)) / a
ev = ev + 2
while od < S:
propVector[od] = (10**(-10)) * Roots[od] / a
tunnVector[od] = (10**(-10)) * (quantumFn.radFunction(
Roots[od], R)) / a
od = od + 2
print("Propagation 'k' vectors")
print(propVector)
print("Tunneling 'K' vectors")
print(tunnVector)
Bcoeff = np.zeros(S)
StateEnergy = np.zeros(S)
l = 0
while l < S:
Bcoeff[l] = quantumFn.Beven(a * 10**(10), propVector[l],
tunnVector[l])
StateEnergy[l] = -1 * quantumFn.energy(
quantumFn.radFunction(Roots[l], R), R, V)
l = l + 2
l = 1
while l < S:
Bcoeff[l] = quantumFn.Bodd(a * 10**(10), propVector[l],
tunnVector[l])
StateEnergy[l] = -1 * quantumFn.energy(
quantumFn.radFunction(Roots[l], R), R, V)
l = l + 2
print("Coefficients")
print(Bcoeff)
print("Energies")
print(StateEnergy)
z = 0
r1 = np.arange((-2 * a * 10**(10)), (-a * 10**(10)), 0.0001)
r2 = np.arange((-a * 10**(10)), (a * 10**(10)), 0.0001)
r3 = np.arange((a * 10**(10)), (2 * a * 10**(10)), 0.0001)
color = ["r", "b", "g", "c", "m", "y", "k"] #This is the color array
c = 0
while z < S:
if c == 6:
c = 0
if z % 2 == 1:
#Note that this file plots the density functions
#Of the states
plt1 = quantumFn.op1(Bcoeff[z], tunnVector[z], propVector[z],
(a * 10**(10)))
plt2 = quantumFn.op2(Bcoeff[z], propVector[z])
plt3 = quantumFn.op3(Bcoeff[z], tunnVector[z], propVector[z],
(a * 10**(10)))
plt.plot(r1,
plt1(r1) + StateEnergy[z], color[c], r2,
plt2(r2) + StateEnergy[z], color[c], r3,
plt3(r3) + StateEnergy[z], color[c])
else:
plt1 = quantumFn.ep1(Bcoeff[z], tunnVector[z], propVector[z],
(a * 10**(10)))
plt2 = quantumFn.ep2(Bcoeff[z], propVector[z])
plt3 = quantumFn.ep3(Bcoeff[z], tunnVector[z], propVector[z],
(a * 10**(10)))
plt.plot(r1,
plt1(r1) + StateEnergy[z], color[c], r2,
plt2(r2) + StateEnergy[z], color[c], r3,
plt3(r3) + StateEnergy[z], color[c])
z = z + 1
c = c + 1
plt.xlabel("Distance (in Angstrom)")
return plt.show()
import quantumFn
from matplotlib import animation
h = 6.626 * 10**(-34) #These are some constants
h_bar = h / (2 * np.pi) #Specifically, Planck's Constant
#This initializes the parameters of the problem
m = (9.11 * 10**(-31)) * float(
input("Mass of particle (X times the mass of electron): ")
) #The mass is based on the electron
V = (1.602 * 10**(-19)) * float(input("Depth of well (eV): "))
a = (10**(-10)) * float(input("Half width of well centered at x=0 (A): "))
#Defines the "radius" based on the parameters
#Which will be used to determine the roots
R = quantumFn.radius(m, a, V)
x = 0
i = 1
j = 0
while R > i * np.pi:
i = i + 1
while R > (1 + 2 * j) * np.pi / 2:
j = j + 1
S = i + j
print(str(S) + " root(s) in total.")
#Initializes the "x" coord of the even and odd roots
evenRoot = np.zeros(i)
oddRoot = np.zeros(j)