"and a ${3} \\times\\,{3}$ matrix"
.format("", l, j, order))
for (i, problem) in enumerate(problems):
print problem.name
plt.subplot(1, 2, i+1)
plt.title(problem.name)
plt.ylabel(r'$r^2|\Psi|^2$')
plt.xlabel(r'$r$')
plt.show(block=False)
for (i, basis) in enumerate(bases):
if basis is osc:
omega = osc.optimal_osc_freq(problem, l, j)
H = calc.hamiltonian(osc.H_element, args=(problem, omega, l, j), order=order)
basis_function = basis.gen_basis_function(problem, omega, l=l, j=j)
else:
H = calc.hamiltonian(basis.H_element, args=(step_size, problem, l, j), order=order)
basis_function = basis.gen_basis_function(step_size, problem, l=l, j=j)
energy, eigvecs = calc.energies(H)
lowest_energy = energy[0] * problem.eV_factor
print basis.name, "lowest energy:", lowest_energy, "eV"
wavefunction = calc.gen_wavefunction(eigvecs[:, 0], basis_function)
wavefunction = calc.normalize(wavefunction, 0, 10, weight=lambda r: r**2)
plt.plot(r, r**2 * absq(wavefunction(r)), label = basis.name)
plt.legend()
plt.draw()
plt.show() # pause when done
from __future__ import division
from imports import *
import nhqm.bases.mom_space as mom
from nhqm.problems import He5
import nhqm.calculations.QM as calc
problem = He5.problem
problem.V0 = -70
k_max = 2.5
steps = 20
lowest_energy = sp.empty(steps)
orders = sp.arange(steps) + 1
l = 0
j = .5
for (i, order) in enumerate(orders):
step = k_max / order
H = calc.hamiltonian(mom.H_element, \
args=(step, problem, l, j), order=order)
energy, eigvecs = calc.energies(H)
lowest_energy[i] = energy[0] # MeV
print order
print lowest_energy[-1]
plt.plot(orders, lowest_energy)
plt.title(r"He5, $l = {0}$, $j = {1}$, $V_0 = {2}$MeV".format(l, j, problem.V0))
plt.xlabel(r"Matrix dimension N ($N \times N$)")
plt.ylabel(r"Lowest energy / MeV")
plt.show()
from __future__ import division
from imports import *
import nhqm.bases.mom_space as mom
from nhqm.problems import He5
import nhqm.calculations.QM as calc
problem = He5.problem
steps = 50
lowest_energy = sp.empty(steps)
V0s = sp.linspace(-70, 0, steps)
l = 0
j = .5
k_max = 4
order = 20
step_size = k_max / order
plt.title(r"He5, $l = {0}$, $j = {1}$".format(l, j))
plt.xlabel(r"Potential well depth V0 / MeV")
plt.ylabel(r"Ground state energy E / MeV")
for (i, V0) in enumerate(V0s):
problem.V0 = V0
H = calc.hamiltonian(mom.H_element, args=(problem, step_size, l, j), order=order)
energy, eigvecs = calc.energies(H)
lowest_energy[i] = energy[0]
print V0
plt.plot(V0s, lowest_energy)
plt.show()
