Source code for sympy.physics.quantum.innerproduct

"""Symbolic inner product."""

from __future__ import print_function, division

from sympy import Expr, conjugate
from sympy.printing.pretty.stringpict import prettyForm
from sympy.physics.quantum.dagger import Dagger
from sympy.physics.quantum.state import KetBase, BraBase

__all__ = [

# InnerProduct is not an QExpr because it is really just a regular commutative
# number. We have gone back and forth about this, but we gain a lot by having
# it subclass Expr. The main challenges were getting Dagger to work
# (we use _eval_conjugate) and represent (we can use atoms and subs). Having
# it be an Expr, mean that there are no commutative QExpr subclasses,
# which simplifies the design of everything.

[docs]class InnerProduct(Expr): """An unevaluated inner product between a Bra and a Ket [1]. Parameters ========== bra : BraBase or subclass The bra on the left side of the inner product. ket : KetBase or subclass The ket on the right side of the inner product. Examples ======== Create an InnerProduct and check its properties: >>> from sympy.physics.quantum import Bra, Ket, InnerProduct >>> b = Bra('b') >>> k = Ket('k') >>> ip = b*k >>> ip <b|k> >>> ip.bra <b| >>> ip.ket |k> In simple products of kets and bras inner products will be automatically identified and created:: >>> b*k <b|k> But in more complex expressions, there is ambiguity in whether inner or outer products should be created:: >>> k*b*k*b |k><b|*|k>*<b| A user can force the creation of a inner products in a complex expression by using parentheses to group the bra and ket:: >>> k*(b*k)*b <b|k>*|k>*<b| Notice how the inner product <b|k> moved to the left of the expression because inner products are commutative complex numbers. References ========== .. [1] http://en.wikipedia.org/wiki/Inner_product """ is_complex = True def __new__(cls, bra, ket): if not isinstance(ket, KetBase): raise TypeError('KetBase subclass expected, got: %r' % ket) if not isinstance(bra, BraBase): raise TypeError('BraBase subclass expected, got: %r' % ket) obj = Expr.__new__(cls, bra, ket) return obj @property def bra(self): return self.args[0] @property def ket(self): return self.args[1] def _eval_conjugate(self): return InnerProduct(Dagger(self.ket), Dagger(self.bra)) def _sympyrepr(self, printer, *args): return '%s(%s,%s)' % (self.__class__.__name__, printer._print(self.bra, *args), printer._print(self.ket, *args)) def _sympystr(self, printer, *args): sbra = str(self.bra) sket = str(self.ket) return '%s|%s' % (sbra[:-1], sket[1:]) def _pretty(self, printer, *args): # Print state contents bra = self.bra._print_contents_pretty(printer, *args) ket = self.ket._print_contents_pretty(printer, *args) # Print brackets height = max(bra.height(), ket.height()) use_unicode = printer._use_unicode lbracket, _ = self.bra._pretty_brackets(height, use_unicode) cbracket, rbracket = self.ket._pretty_brackets(height, use_unicode) # Build innerproduct pform = prettyForm(*bra.left(lbracket)) pform = prettyForm(*pform.right(cbracket)) pform = prettyForm(*pform.right(ket)) pform = prettyForm(*pform.right(rbracket)) return pform def _latex(self, printer, *args): bra_label = self.bra._print_contents_latex(printer, *args) ket = printer._print(self.ket, *args) return r'\left\langle %s \right. %s' % (bra_label, ket) def doit(self, **hints): try: r = self.ket._eval_innerproduct(self.bra, **hints) except NotImplementedError: try: r = conjugate( self.bra.dual._eval_innerproduct(self.ket.dual, **hints) ) except NotImplementedError: r = None if r is not None: return r return self