ó ¡¼™\c@ s|dZddlmZmZddlmZmZmZmZm Z m Z m Z ddl m Z ddlmZmZmZddlmZmZmZmZmZmZmZddgZieeefƒe6eeefƒe6eeefƒe6e e6eeeefƒe 6e e 6ee6Zed „ejƒDƒƒZd „Z d „Z!d „Z"d „Z#d„Z$d„Z%dS(s A module for mapping operators to their corresponding eigenstates and vice versa It contains a global dictionary with eigenstate-operator pairings. If a new state-operator pair is created, this dictionary should be updated as well. It also contains functions operators_to_state and state_to_operators for mapping between the two. These can handle both classes and instances of operators and states. See the individual function descriptions for details. TODO List: - Update the dictionary with a complete list of state-operator pairs iÿÿÿÿ(tprint_functiontdivision(tXOptYOptZOptXKettPxOptPxKett PositionKet3D(tOperator(t StateBasetBraBasetKet(tJxOptJyOptJzOptJ2OptJxKettJyKettJzKettoperators_to_statetstate_to_operatorscc s!|]\}}||fVqdS(N((t.0tktv((s@lib/python2.7/site-packages/sympy/physics/quantum/operatorset.pys .sc K sát|tƒp*t|tƒp*t|tƒs<tdƒ‚nt|tƒr\x;|D]3}t|tƒpst|tƒsRtdƒ‚qRqRWt|ƒ}|tkrÿy<g|D]}|ƒ^q«}tt|t|ƒ|}Wntk rút|}nX|Sg|D]}t|ƒ^q}t|ƒ} | tkrOtt| ||}nd}|Sn|tkr­y#|ƒ} tt|| |}Wntk r¨t|}nX|St|ƒtkrÙttt|ƒ||SdSdS(s. Returns the eigenstate of the given operator or set of operators A global function for mapping operator classes to their associated states. It takes either an Operator or a set of operators and returns the state associated with these. This function can handle both instances of a given operator or just the class itself (i.e. both XOp() and XOp) There are multiple use cases to consider: 1) A class or set of classes is passed: First, we try to instantiate default instances for these operators. If this fails, then the class is simply returned. If we succeed in instantiating default instances, then we try to call state._operators_to_state on the operator instances. If this fails, the class is returned. Otherwise, the instance returned by _operators_to_state is returned. 2) An instance or set of instances is passed: In this case, state._operators_to_state is called on the instances passed. If this fails, a state class is returned. If the method returns an instance, that instance is returned. In both cases, if the operator class or set does not exist in the state_mapping dictionary, None is returned. Parameters ========== arg: Operator or set The class or instance of the operator or set of operators to be mapped to a state Examples ======== >>> from sympy.physics.quantum.cartesian import XOp, PxOp >>> from sympy.physics.quantum.operatorset import operators_to_state >>> from sympy.physics.quantum.operator import Operator >>> operators_to_state(XOp) |x> >>> operators_to_state(XOp()) |x> >>> operators_to_state(PxOp) |px> >>> operators_to_state(PxOp()) |px> >>> operators_to_state(Operator) |psi> >>> operators_to_state(Operator()) |psi> s%Argument is not an Operator or a set!sSet is not all Operators!N( t isinstanceR tsett issubclasstNotImplementedErrort frozensett op_mappingt _get_statettypetNone( t operatorstoptionststopstopt op_instancestrettottmptclassest op_instance((s@lib/python2.7/site-packages/sympy/physics/quantum/operatorset.pyR1s@6          cK s“t|tƒpt|tƒs-tdƒ‚n|tkrŒt|ƒ}y t|tt|ƒ|}Wq‰ttfk rˆt|}q‰Xnýt |ƒtkrÃt|ttt |ƒƒ|}nÆt|t ƒr|j ƒtkrt|tt|j ƒƒƒ}nƒt|t ƒrƒ|j ƒtkrƒt|ƒ}y#t|tt|j ƒƒƒ}Wq‰ttfk rt|j ƒ}q‰Xnd}t|ƒS(s` Returns the operator or set of operators corresponding to the given eigenstate A global function for mapping state classes to their associated operators or sets of operators. It takes either a state class or instance. This function can handle both instances of a given state or just the class itself (i.e. both XKet() and XKet) There are multiple use cases to consider: 1) A state class is passed: In this case, we first try instantiating a default instance of the class. If this succeeds, then we try to call state._state_to_operators on that instance. If the creation of the default instance or if the calling of _state_to_operators fails, then either an operator class or set of operator classes is returned. Otherwise, the appropriate operator instances are returned. 2) A state instance is returned: Here, state._state_to_operators is called for the instance. If this fails, then a class or set of operator classes is returned. Otherwise, the instances are returned. In either case, if the state's class does not exist in state_mapping, None is returned. Parameters ========== arg: StateBase class or instance (or subclasses) The class or instance of the state to be mapped to an operator or set of operators Examples ======== >>> from sympy.physics.quantum.cartesian import XKet, PxKet, XBra, PxBra >>> from sympy.physics.quantum.operatorset import state_to_operators >>> from sympy.physics.quantum.state import Ket, Bra >>> state_to_operators(XKet) X >>> state_to_operators(XKet()) X >>> state_to_operators(PxKet) Px >>> state_to_operators(PxKet()) Px >>> state_to_operators(PxBra) Px >>> state_to_operators(XBra) X >>> state_to_operators(Ket) O >>> state_to_operators(Bra) O sArgument is not a state!N( RR RRt state_mappingt _make_defaultt_get_opst _make_sett TypeErrorR R t dual_classR!(tstateR#t state_instR(((s@lib/python2.7/site-packages/sympy/physics/quantum/operatorset.pyR–s0;  !! cC s+y |ƒ}Wntk r&|}nX|S(N(t Exception(texprR(((s@lib/python2.7/site-packages/sympy/physics/quantum/operatorset.pyR.îs    cK s:y|j||}Wntk r5t|ƒ}nX|S(N(t_operators_to_stateRR.(t state_classR%R#R(((s@lib/python2.7/site-packages/sympy/physics/quantum/operatorset.pyR÷s  cK s”y|j||}WnNtk rft|tttfƒrWtd„|Dƒƒ}qgt|ƒ}nXt|tƒrt|ƒdkr|dS|S(Ncs s|]}t|ƒVqdS(N(R.(Rtx((s@lib/python2.7/site-packages/sympy/physics/quantum/operatorset.pys sii(t_state_to_operatorsRRRttupleRR.tlen(R4t op_classesR#R(((s@lib/python2.7/site-packages/sympy/physics/quantum/operatorset.pyR/s !cC s*t|tttfƒr"t|ƒS|SdS(N(RR;tlistRR(R%((s@lib/python2.7/site-packages/sympy/physics/quantum/operatorset.pyR0s N(&t__doc__t __future__RRtsympy.physics.quantum.cartesianRRRRRRRtsympy.physics.quantum.operatorR tsympy.physics.quantum.stateR R R tsympy.physics.quantum.spinR RRRRRRt__all__RR-tdicttitemsRRRR.RR/R0(((s@lib/python2.7/site-packages/sympy/physics/quantum/operatorset.pyts*44   e X