def squarepot(VV = np.array([0,1,0]), xx = np.array([-2, -1, 1, 2]), neigs = 40):
"""
Compute resonances of a one-dimensional piecewise-constant potential.
The value of the potential will be VV(i) on the interval ( xx(i), xx(i+1) ).
Input:
VV -- Value of the potential on each interval
xx -- Coordinates of the interval endpoints
neigs -- Max eigenvalues or resonances to be computed (default: 40)
Output:
l -- Vector of resolved resonance poles in the lambda (wave number) plane
"""
elt = square_well(xx, VV)
f, axarr = plt.subplots(2)
plot_potential1( VV, xx, axarr[0] )
l = checked_resonances(elt, neigs)
# #TODO: Fix plot point sizes
l_full = checked_resonances(elt)
axarr[1].scatter(l_full.real, l_full.imag)
axarr[1].set_title('Pole locations')
# plt.axis('equal')
plt.show()
return l
def data_gen():
t = 0.0
for pot in potentials:
elt = square_well(ab=[-pot])
(x,V) = plot_potential(elt)
l = checked_resonances(elt, 20)
yield x, V, l.real, l.imag
from plotting import plot_potential
from square_well import square_well
from compute_scatter import compute_scatter
from plotting import plot_fields
from plotting import animate_wave
print 'In the first example, we show how the eigenvalues and resonances \
change as the depth of a square potential well changes.'
raw_input('Press Enter to begin\n')
potentials = np.linspace(6,10,20)
sq_potential(potentials)
print '\nNow we consider the scattering from a plane wave of the form exp(-ikx), where k = pi. The real part of the scattered wave is in red; the imaginary part is in blue.'
raw_input('Press Enter to begin\n')
elt = square_well([-10])
u = compute_scatter(elt, -np.pi)
(x,V) = plot_potential(elt)
x_u = plot_fields(elt, u)
fig, (ax1, ax2) = plt.subplots(2,1)
# intialize two line objects (one in each axes)
ax1.set_ylim(-11, 1)
for ax in [ax1, ax2]:
ax.set_xlim(-2, 2)
ax.grid()
ax1.plot(x, V, marker='o', linestyle='-',color='r')
ax2.plot(x_u, u.real, marker='o', linestyle='-',color='r')
ax2.plot(x_u, u.imag, marker='o', linestyle='-',color='b')
plt.show()
