def radial_wave_func(n, l, r):
# a=c.physical_constants['Bohr radius'][0]
n = str(n)
l = str(l)
nl = n + l
A = a[nl]
B = bohr(nl, r)
C = c(nl, r)
output = round(A * B * C, 5)
return output
def angular_wave_func(m, l, theta, phi):
m = str(m)
l = str(l)
ml = m + l
Ax = "a" + ml
A = round(a(Ax, m), 5)
B = round(b(ml, theta), 5)
C = round(c(m, theta), 5)
D = round(d(m, phi), 5)
Y = round(A * B * C * D, 5)
return Y
def radial_wave_func(n,l,r):
import scipy.constants as c
# global constants
b = c.physical_constants['Bohr radius'][0] # Bohr's radius
# normalised means just the term a^(-3/2) is 1
a = {
"10": 2,
"20": np.sqrt(1 / 2),
"21": np.sqrt(1 / 24),
"30": np.sqrt(4 / 19683),
"31": np.sqrt(64 / 4374),
"32": np.sqrt(16 / 196830),
"40": np.sqrt(1 / 16),
"41": np.sqrt(5 / 768),
"42": np.sqrt(1 / 20480),
"43": np.sqrt(1 / 20643840)
}
def bohr(x1, x2): # x1 - name x2 - r(float)
if (x1 == "10"):
output = 1
return output
elif (x1 == "20"):
output = 1 - (x2 / (2 * b))
return output
elif (x1 == "21"):
output = x2 / b
return output
elif (x1 == "30"):
output = 27 - (18 * (x2 / b)) + (2 * ((x2 / b) ** 2))
return output
elif (x1 == "31"):
output = (1 - (x2 / (6 * b))) * (x2 / b)
return output
elif (x1 == "32"):
output = (x2 / b) ** 2
return output
elif (x1 == "40"):
output = 1 - ((3 / 4) * (x2 / b)) + ((1 / 8) * ((x2 / b) ** 2)) - ((1 / 192) * ((x2 / b) ** 3))
return output
elif (x1 == "41"):
output = (x2 / b) * (1 - ((1 / 4) * (x2 / b)) + ((1 / 80) * ((x2 / b) ** 2)))
return output
elif (x1 == "42"):
output = ((x2 / b) ** 2) * (1 - (1 / 12) * (x2 / b))
return output
elif (x1 == "43"):
output = (x2 / b) ** 3
return output
else:
print("value B error")
return
def c(x1, x2): # x1 - name x2 - r(float)
x1 = int(x1[0])
output = np.exp((-1) * (x2 / (x1 * b)))
return output
# a=c.physical_constants['Bohr radius'][0]
n = str(n)
l = str(l)
nl = n + l
A = a[nl]
B = bohr(nl, r)
C = c(nl, r)
output = round(A * B * C, 5)
return output
def angular_wave_func(m,l,theta,phi):
# y= a * b * c * d
# global constants
pi = math.pi
# constants for a
aDict = {
"a00": np.sqrt(1 / (4 * pi)),
"a01": np.sqrt(3 / (4 * pi)),
"a02": np.sqrt(5 / (16 * pi)),
"a03": np.sqrt(7 / (16 * pi)),
"a11": np.sqrt(3 / (8 * pi)),
"a12": np.sqrt(15 / (8 * pi)),
"a13": np.sqrt(21 / (64 * pi)),
"a22": np.sqrt(15 / (32 * pi)),
"a23": np.sqrt(105 / (32 * pi)),
"a33": np.sqrt(35 / (64 * pi))
}
def a(x1, x2): # x1 - dictionary input x2 - m
x2 = int(x2)
if (x2 == 1) or (x2 == 3):
neg = -1
else:
neg = 1
output = neg * aDict[x1]
return output
# constants for b
def b(x1, x2): # x1 - ml(str) x2 - theta(int)
x2 = float(x2)
if x1 == "00":
b00 = float(1)
return b00
elif x1 == "01":
b01 = float(np.cos(x2))
return b01
elif x1 == "02":
b02 = float((3 * (np.cos(x2) ** 2)) - 1)
return b02
elif x1 == "03":
b03 = float((5 * (np.cos(x2) ** 3)) - (3 * np.cos(x2)))
return b03
elif x1 == "11":
b11 = float(1)
return b11
elif x1 == "12":
b12 = float(np.cos(x2))
return b12
elif x1 == "13":
b13 = float((5 * (np.cos(x2)) ** 2) - 1)
return b13
elif x1 == "22":
b22 = float(1)
return b22
elif x1 == "23":
b23 = float(np.cos(x2))
return b23
elif x1 == "33":
b33 = float(1)
return b33
else:
print("variable b error")
return
def c(x1, x2): # x1 - m(str) x2 - theta(int)
x1 = abs(int(x1))
output = float((np.sin(x2)) ** x1)
return output
def d(x1, x2): # x1 - m(str) x2 - phi(int)
x1 = int(x1)
x = x2 * x1
output = np.cos(x) + (1j) * round(np.sin(x), 5)
return output
m = str(m)
l = str(l)
ml = m + l
Ax = "a" + ml
A = round(a(Ax, m), 5)
B = round(b(ml, theta), 5)
C = round(c(m, theta), 5)
D = round(d(m, phi), 5)
Y = round(A * B * C * D, 5)
return Y