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Mini Shell
Mini Shell
"""1D quantum particle in a box."""
from sympy import Symbol, pi, sqrt, sin, Interval, S
from sympy.physics.quantum.operator import HermitianOperator
from sympy.physics.quantum.state import Ket, Bra
from sympy.physics.quantum.constants import hbar
from sympy.functions.special.tensor_functions import KroneckerDelta
from sympy.physics.quantum.hilbert import L2
m = Symbol('m')
L = Symbol('L')
__all__ = [
'PIABHamiltonian',
'PIABKet',
'PIABBra'
]
class PIABHamiltonian(HermitianOperator):
"""Particle in a box Hamiltonian operator."""
@classmethod
def _eval_hilbert_space(cls, label):
return L2(Interval(S.NegativeInfinity, S.Infinity))
def _apply_operator_PIABKet(self, ket, **options):
n = ket.label[0]
return (n**2*pi**2*hbar**2)/(2*m*L**2)*ket
class PIABKet(Ket):
"""Particle in a box eigenket."""
@classmethod
def _eval_hilbert_space(cls, args):
return L2(Interval(S.NegativeInfinity, S.Infinity))
@classmethod
def dual_class(self):
return PIABBra
def _represent_default_basis(self, **options):
return self._represent_XOp(None, **options)
def _represent_XOp(self, basis, **options):
x = Symbol('x')
n = Symbol('n')
subs_info = options.get('subs', {})
return sqrt(2/L)*sin(n*pi*x/L).subs(subs_info)
def _eval_innerproduct_PIABBra(self, bra):
return KroneckerDelta(bra.label[0], self.label[0])
class PIABBra(Bra):
"""Particle in a box eigenbra."""
@classmethod
def _eval_hilbert_space(cls, label):
return L2(Interval(S.NegativeInfinity, S.Infinity))
@classmethod
def dual_class(self):
return PIABKet
Zerion Mini Shell 1.0