ó ¡¼™\c@sýdZddlmZmZmZmZmZddlmZddlm Z m Z m Z m Z m Z ddlmZdddd d gZdefd „ƒYZde fd „ƒYZde fd „ƒYZd e fd„ƒYZd e fd„ƒYZdS(sBosonic quantum operators.iÿÿÿÿ(tMultIntegertexptsqrtt conjugate(tOperator(t HilbertSpacet FockSpacetKettBratIdentityOperator(tKroneckerDeltatBosonOpt BosonFockKett BosonFockBratBosonCoherentKettBosonCoherentBracBsŒeZdZed„ƒZed„ƒZed„ƒZd„Zd„Z d„Z d„Z d„Z d „Z d „Zd „Zd „ZRS( sA bosonic operator that satisfies [a, Dagger(a)] == 1. Parameters ========== name : str A string that labels the bosonic mode. annihilation : bool A bool that indicates if the bosonic operator is an annihilation (True, default value) or creation operator (False) Examples ======== >>> from sympy.physics.quantum import Dagger, Commutator >>> from sympy.physics.quantum.boson import BosonOp >>> a = BosonOp("a") >>> Commutator(a, Dagger(a)).doit() 1 cCs |jdS(Ni(targs(tself((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pytname)scCst|jdƒS(Ni(tboolR(R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pytis_annihilation-scCs dtfS(Nta(tTrue(R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt default_args1scOst|ƒdkr%td|ƒ‚nt|ƒdkrP|dtdƒf}nt|ƒdkr|dt|dƒf}ntj||ŒS(Niis"1 or 2 parameters expected, got %si(ii(tlent ValueErrorRRt__new__(tclsRthints((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR5scKsV|j|jkr2|j rR|jrRtdƒSn d|krR|drRtdƒSdS(Niÿÿÿÿt independenti(RRRtNone(RtotherR((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt_eval_commutator_BosonOpAs   cKs tdƒS(Ni(R(RR R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt_eval_commutator_FermionOpMscKs&d|kr"|dr"d||SdS(NRi(R(RR R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt_eval_anticommutator_BosonOpPs cCstt|jƒ|j ƒS(N(R tstrRR(R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt _eval_adjointWscCs“|tdƒkr|St|tƒr†td„|jDƒƒ}td„|jDƒƒ}|}x|D]}||}qdWt|Œ|St||ƒS(Nicss|]}|jr|VqdS(N(tis_commutative(t.0targ((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pys `scss|]}|js|VqdS(N(R&(R'R(((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pys as(R t isinstanceRttupleR(RR targs1targs2txty((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt__mul__Zs cGs/|jrdt|jƒSdt|jƒSdS(Ns{%s}s{{%s}^\dagger}(RR$R(RtprinterR((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt_print_contents_latexis cGs/|jrdt|jƒSdt|jƒSdS(Ns%ss Dagger(%s)(RR$R(RR0R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt_print_contentsos cGsHddlm}|j|jd|Œ}|jr6|S||dƒSdS(Niÿÿÿÿ(t prettyFormiu†(t sympy.printing.pretty.stringpictR3t_printRR(RR0RR3tpform((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt_print_contents_prettyus  (t__name__t __module__t__doc__tpropertyRRt classmethodRRR!R"R#R%R/R1R2R7(((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR s      cBsVeZdZd„Zed„ƒZed„ƒZed„ƒZd„Z d„Z RS(svFock state ket for a bosonic mode. Parameters ========== n : Number The Fock state number. cCstj||ƒS(N(RR(Rtn((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR‰scCs |jdS(Ni(tlabel(R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR=ŒscCstS(N(R(R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt dual_classscCstƒS(N(R(RR>((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt_eval_hilbert_space”scKst|j|jƒS(N(R R=(RtbraR((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt_eval_innerproduct_BosonFockBra˜scKsM|jr't|jƒt|jdƒSt|jdƒt|jdƒSdS(Ni(RRR=R (Rtoptoptions((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt_apply_operator_BosonOp›s ( R8R9R:RR;R=R<R?R@RBRE(((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR ~s   cBsDeZdZd„Zed„ƒZed„ƒZed„ƒZRS(svFock state bra for a bosonic mode. Parameters ========== n : Number The Fock state number. cCstj||ƒS(N(R R(RR=((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR­scCs |jdS(Ni(R>(R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR=°scCstS(N(R (R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR?´scCstƒS(N(R(RR>((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR@¸s( R8R9R:RR;R=R<R?R@(((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR¢s   cBsVeZdZd„Zed„ƒZed„ƒZed„ƒZd„Z d„Z RS(sœCoherent state ket for a bosonic mode. Parameters ========== alpha : Number, Symbol The complex amplitude of the coherent state. cCstj||ƒS(N(RR(Rtalpha((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyRÈscCs |jdS(Ni(R>(R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyRFËscCstS(N(R(R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR?ÏscCstƒS(N(R(RR>((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR@ÓscKse|j|jkrtdƒStt|jƒdt|jƒddt|jƒ|j dƒSdS(Nii(RFRRtabsR(RRAR((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyt#_eval_innerproduct_BosonCoherentBra×s cKs|jr|j|SdSdS(N(RRFR(RRCRD((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyREÝs  ( R8R9R:RR;RFR<R?R@RHRE(((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR½s   cBs>eZdZd„Zed„ƒZed„ƒZd„ZRS(sœCoherent state bra for a bosonic mode. Parameters ========== alpha : Number, Symbol The complex amplitude of the coherent state. cCstj||ƒS(N(R R(RRF((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyRïscCs |jdS(Ni(R>(R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyRFòscCstS(N(R(R((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyR?öscKs|js|j|SdSdS(N(RRFR(RRCRD((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyREús  ( R8R9R:RR;RFR<R?RE(((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyRäs   N(R:tsympyRRRRRtsympy.physics.quantumRRRRR R t(sympy.functions.special.tensor_functionsR t__all__R R RRR(((s:lib/python2.7/site-packages/sympy/physics/quantum/boson.pyts(( l$'