def __init__(self, innerproduct=None):
r"""Initialize a new :py:class:`ObservablesHAWP` instance for observable computation
of Hagedorn wavepackets.
:param innerproduct: An inner product for computing the integrals. The inner product is only used for
the computation of the potential energy :math:`\langle\Psi|V(x)|\Psi\rangle`
but not for the kinetic energy.
:type innerproduct: A :py:class:`InnerProduct` subclass instance.
"""
# A innerproduct to compute the integrals
if innerproduct is not None:
self._innerproduct = innerproduct
self._gradient = GradientHAWP()
class ObservablesHAWP(Observables):
r"""This class implements observable computation for Hagedorn wavepackets :math:`\Psi`.
"""
def __init__(self, innerproduct=None):
r"""Initialize a new :py:class:`ObservablesHAWP` instance for observable computation
of Hagedorn wavepackets.
:param innerproduct: An inner product for computing the integrals. The inner product is only used for
the computation of the potential energy :math:`\langle\Psi|V(x)|\Psi\rangle`
but not for the kinetic energy.
:type innerproduct: A :py:class:`InnerProduct` subclass instance.
"""
# A innerproduct to compute the integrals
if innerproduct is not None:
self._innerproduct = innerproduct
self._gradient = GradientHAWP()
def set_innerproduct(self, innerproduct):
r"""Set the innerproduct.
:param innerproduct: An innerproduct for computing the integrals. The inner product is only used for
the computation of the potential energy :math:`\langle\Psi|V(x)|\Psi\rangle`
but not for the kinetic energy.
:type innerproduct: A :py:class:`InnerProduct` subclass instance.
"""
self._innerproduct = innerproduct
def norm(self, wavepacket, component=None, summed=False):
r"""Calculate the :math:`L^2` norm :math:`\langle\Psi|\Psi\rangle` of the wavepacket :math:`\Psi`.
Note: this method is just a shortcut and calls the :py:meth:`HagedornWavepacketBase.norm` method
of the given wavepacket.
:param wavepacket: The wavepacket :math:`\Psi` of which we compute the norm.
:type wavepacket: A :py:class:`HagedornWavepacketBase` subclass instance.
:param component: The index :math:`i` of the component :math:`\Phi_i` whose norm is calculated.
The default value is ``None`` which means to compute the norms of all :math:`N` components.
:type component: int or ``None``.
:param summed: Whether to sum up the norms :math:`\langle\Phi_i|\Phi_i\rangle` of the
individual components :math:`\Phi_i`.
:type summed: Boolean, default is ``False``.
:type summed: Boolean, default is ``False``.
:return: The norm of :math:`\Psi` or the norm of :math:`\Phi_i` or a list with the :math:`N`
norms of all components. Depending on the values of ``component`` and ``summed``.
"""
return wavepacket.norm(component=component, summed=summed)
def kinetic_energy(self, wavepacket, component=None, summed=False):
r"""Compute the kinetic energy :math:`E_{\text{kin}} := \langle\Psi|T|\Psi\rangle`
of the different components :math:`\Phi_i` of the wavepacket :math:`\Psi`.
:param wavepacket: The wavepacket :math:`\Psi` of which we compute the kinetic energy.
:type wavepacket: A :py:class:`HagedornWavepacketBase` subclass instance.
:param component: The index :math:`i` of the component :math:`\Phi_i` whose
kinetic energy we want to compute. If set to ``None`` the
computation is performed for all :math:`N` components.
:type component: Integer or ``None``.
:param summed: Whether to sum up the kinetic energies :math:`E_i` of the individual
components :math:`\Phi_i`. Default is ``False``.
:type summed: Boolean
:return: A list with the kinetic energies of the individual components or the
overall kinetic energy of the wavepacket. (Depending on the optional arguments.)
"""
if component is None:
N = wavepacket.get_number_components()
components = xrange(N)
else:
components = [component]
ekin = []
for n in components:
Kprime, cnew = self._gradient.apply_gradient(wavepacket, n)
ekin.append(0.5 * sum(sum(conjugate(cnew)*cnew, axis=1), axis=0))
if summed is True:
ekin = sum(ekin)
elif component is not None:
# Do not return a list for specific single components
ekin = ekin[0]
return ekin
def potential_energy(self, wavepacket, potential, component=None, summed=False):
r"""Compute the potential energy :math:`E_{\text{pot}} := \langle\Psi|V|\Psi\rangle`
of the different components :math:`\Phi_i` of the wavepacket :math:`\Psi`.
:param wavepacket: The wavepacket :math:`\Psi` of which we compute the potential energy.
:type wavepacket: A :py:class:`HagedornWavepacketBase` subclass instance.
:param potential: The potential :math:`V(x)`. (Actually, not the potential object itself
but one of its ``V.evaluate_*`` methods.)
:param component: The index :math:`i` of the component :math:`\Phi_i` whose
potential energy we want to compute. If set to ``None`` the
computation is performed for all :math:`N` components.
:type component: Integer or ``None``.
:param summed: Whether to sum up the potential energies :math:`E_i` of the individual
components :math:`\Phi_i`. Default is ``False``.
:type summed: Boolean
:return: A list with the potential energies of the individual components or the
overall potential energy of the wavepacket. (Depending on the optional arguments.)
"""
N = wavepacket.get_number_components()
# TODO: Better take 'V' instead of 'V.evaluate_at' as argument?
#f = partial(potential.evaluate_at, as_matrix=True)
f = partial(potential, as_matrix=True)
# Compute the brakets for each component
if component is not None:
Q = self._innerproduct.quadrature(wavepacket, operator=f, diag_component=component, eval_at_once=True)
else:
Q = self._innerproduct.quadrature(wavepacket, operator=f, eval_at_once=True)
# And don't forget the summation in the matrix multiplication of 'operator' and 'ket'
# TODO: Should this go inside the innerproduct?
tmp = map(squeeze, Q)
epot = [ sum(tmp[i*N:(i+1)*N]) for i in xrange(N) ]
if summed is True:
epot = sum(epot)
elif component is not None:
# Do not return a list for specific single components
epot = epot[0]
return epot