def solve_schroedinger(mesh, l=0, Z=1, eqn_type="R", eig_num=4):
"""
Solves the Schroedinger equation on the given mesh.
Returns the energies and eigenfunctions.
"""
# TODO: return the eigenfunctions as FESolutions
N_dof = mesh.assign_dofs()
A = CSCMatrix(N_dof)
B = CSCMatrix(N_dof)
assemble_schroedinger(mesh, A, B, l=l, Z=Z, eqn_type=eqn_type)
eigs = solve_eig_scipy(A.to_scipy_csc(), B.to_scipy_csc())
eigs = eigs[:eig_num]
energies = [E for E, eig in eigs]
#print energies
assert len(eigs) == eig_num
eigs = [eig for E, eig in eigs]
return N_dof, array(energies), eigs
def solve_schroedinger(mesh, l=0, Z=1, eqn_type="R", eig_num=4):
"""
Solves the Schroedinger equation on the given mesh.
Returns the energies and eigenfunctions.
"""
# TODO: return the eigenfunctions as FESolutions
N_dof = mesh.assign_dofs()
A = CSCMatrix(N_dof)
B = CSCMatrix(N_dof)
assemble_schroedinger(mesh, A, B, l=l, Z=Z, eqn_type=eqn_type)
eigs = solve_eig_scipy(A.to_scipy_csc(), B.to_scipy_csc())
eigs = eigs[:eig_num]
energies = [E for E, eig in eigs]
#print energies
assert len(eigs) == eig_num
eigs = [eig for E, eig in eigs]
return N_dof, array(energies), eigs
def solve_dirac(mesh, kappa=1, Z=1, eig_num=4):
"""
Solves the Dirac equation on the given mesh.
Returns the energies and eigenfunctions.
"""
mesh.set_bc_left_dirichlet(0, 0);
mesh.set_bc_right_dirichlet(0, 0);
N_dof = mesh.assign_dofs()
A = CooMatrix(N_dof)
B = CooMatrix(N_dof)
assemble_dirac(mesh, A, B, kappa=kappa, Z=Z)
eigs = solve_eig_scipy(A.to_scipy_coo(), B.to_scipy_coo())
c = 137.03599911
eigs = [(E, eig) for E, eig in eigs if E > -2*c**2 and E < 0]
eigs = eigs[:eig_num]
#assert len(eigs) == eig_num
energies = [E for E, eig in eigs]
eigs = [eig for E, eig in eigs]
return N_dof, array(energies), eigs
def solve_dirac(mesh, kappa=1, Z=1, eig_num=4):
"""
Solves the Dirac equation on the given mesh.
Returns the energies and eigenfunctions.
"""
mesh.set_bc_left_dirichlet(0, 0)
mesh.set_bc_right_dirichlet(0, 0)
N_dof = mesh.assign_dofs()
A = CooMatrix(N_dof)
B = CooMatrix(N_dof)
assemble_dirac(mesh, A, B, kappa=kappa, Z=Z)
eigs = solve_eig_scipy(A.to_scipy_coo(), B.to_scipy_coo())
c = 137.03599911
eigs = [(E, eig) for E, eig in eigs if E > -2 * c**2 and E < 0]
eigs = eigs[:eig_num]
#assert len(eigs) == eig_num
energies = [E for E, eig in eigs]
eigs = [eig for E, eig in eigs]
return N_dof, array(energies), eigs