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