1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
|
from pathlib import Path
import numpy as np
from numpy.polynomial import Polynomial
from numpy.typing import NDArray
from scipy.interpolate import CubicSpline
from scipy.linalg import eigh_tridiagonal
class Config:
def __init__(self, path):
current_line = 0
# Ensure Path object
if path is not Path:
path = Path(path)
def next_parameter(fd):
'''Read next parameter, ignoring comments or empty lines'''
content = None
nonlocal current_line
while not content:
str = fd.readline()
current_line += 1
index = str.find('#')
content = str[0:index].strip()
return content
with open(path, 'r') as fd:
try:
self.mass = float(next_parameter(fd))
start, end, steps = next_parameter(fd).split()
self.interval = [float(start), float(end), int(steps)]
self.eig_interval = [int(attr) - 1 for attr in next_parameter(fd).split()]
self.interpolation = next_parameter(fd)
npoints = int(next_parameter(fd))
self.points = np.zeros((npoints, 2))
for i in range(npoints):
line = next_parameter(fd)
self.points[i] = np.array([float(comp) for comp in line.split()])
# TODO: don't be a moron, catch only relevant exceptions
except:
print('Syntax error in \'{}\' line {}'.format(path.name, current_line))
raise ValueError()
def potential_interp(interpolation, points):
if interpolation == 'linear':
def line(x):
return np.interp(x, points[:, 0], points[:, 1])
return line
elif interpolation == 'polynomial':
poly = Polynomial.fit(points[:, 0], points[:, 1],
points.shape[0] - 1)
return poly
elif interpolation == 'cspline':
cs = CubicSpline(points[:, 0], points[:, 1])
return cs
raise ValueError()
def build_potential(config: Config):
start, end, steps = config.interval
potential = np.zeros((steps, 2))
potential[:, 0] = np.linspace(start, end, steps)
delta = np.abs(potential[1, 0] - potential[0, 0])
interp = potential_interp(config.interpolation, config.points)
potential[:, 1] = interp(potential[:, 0])
return potential, delta
def solve_schroedinger(mass, potential, delta, eig_interval=None):
'''
returns eigen values and wave functions specified by eig_interval
'''
n = potential.shape[0]
a = 1 / mass / delta**2
w, v = eigh_tridiagonal(a + potential,
-a * np.ones(n - 1, dtype=np.float_) / 2.0,
select='i', select_range=eig_interval)
# Normalize eigenfunctions
for i in range(w.shape[0]):
v[:, i] /= np.sqrt(delta * np.sum(np.abs(v[:, i])**2))
return w, v
|
