281 lines
9.4 KiB
Python
281 lines
9.4 KiB
Python
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""" A module for mapping operators to their corresponding eigenstates
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and vice versa
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It contains a global dictionary with eigenstate-operator pairings.
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If a new state-operator pair is created, this dictionary should be
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updated as well.
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It also contains functions operators_to_state and state_to_operators
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for mapping between the two. These can handle both classes and
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instances of operators and states. See the individual function
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descriptions for details.
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TODO List:
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- Update the dictionary with a complete list of state-operator pairs
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"""
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from sympy.physics.quantum.cartesian import (XOp, YOp, ZOp, XKet, PxOp, PxKet,
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PositionKet3D)
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from sympy.physics.quantum.operator import Operator
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from sympy.physics.quantum.state import StateBase, BraBase, Ket
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from sympy.physics.quantum.spin import (JxOp, JyOp, JzOp, J2Op, JxKet, JyKet,
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JzKet)
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__all__ = [
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'operators_to_state',
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'state_to_operators'
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]
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#state_mapping stores the mappings between states and their associated
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#operators or tuples of operators. This should be updated when new
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#classes are written! Entries are of the form PxKet : PxOp or
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#something like 3DKet : (ROp, ThetaOp, PhiOp)
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#frozenset is used so that the reverse mapping can be made
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#(regular sets are not hashable because they are mutable
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state_mapping = { JxKet: frozenset((J2Op, JxOp)),
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JyKet: frozenset((J2Op, JyOp)),
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JzKet: frozenset((J2Op, JzOp)),
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Ket: Operator,
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PositionKet3D: frozenset((XOp, YOp, ZOp)),
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PxKet: PxOp,
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XKet: XOp }
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op_mapping = {v: k for k, v in state_mapping.items()}
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def operators_to_state(operators, **options):
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""" Returns the eigenstate of the given operator or set of operators
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A global function for mapping operator classes to their associated
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states. It takes either an Operator or a set of operators and
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returns the state associated with these.
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This function can handle both instances of a given operator or
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just the class itself (i.e. both XOp() and XOp)
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There are multiple use cases to consider:
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1) A class or set of classes is passed: First, we try to
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instantiate default instances for these operators. If this fails,
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then the class is simply returned. If we succeed in instantiating
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default instances, then we try to call state._operators_to_state
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on the operator instances. If this fails, the class is returned.
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Otherwise, the instance returned by _operators_to_state is returned.
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2) An instance or set of instances is passed: In this case,
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state._operators_to_state is called on the instances passed. If
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this fails, a state class is returned. If the method returns an
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instance, that instance is returned.
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In both cases, if the operator class or set does not exist in the
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state_mapping dictionary, None is returned.
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Parameters
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==========
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arg: Operator or set
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The class or instance of the operator or set of operators
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to be mapped to a state
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Examples
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========
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>>> from sympy.physics.quantum.cartesian import XOp, PxOp
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>>> from sympy.physics.quantum.operatorset import operators_to_state
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>>> from sympy.physics.quantum.operator import Operator
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>>> operators_to_state(XOp)
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|x>
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>>> operators_to_state(XOp())
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|x>
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>>> operators_to_state(PxOp)
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|px>
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>>> operators_to_state(PxOp())
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|px>
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>>> operators_to_state(Operator)
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|psi>
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>>> operators_to_state(Operator())
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|psi>
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"""
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if not (isinstance(operators, Operator)
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or isinstance(operators, set) or issubclass(operators, Operator)):
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raise NotImplementedError("Argument is not an Operator or a set!")
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if isinstance(operators, set):
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for s in operators:
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if not (isinstance(s, Operator)
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or issubclass(s, Operator)):
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raise NotImplementedError("Set is not all Operators!")
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ops = frozenset(operators)
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if ops in op_mapping: # ops is a list of classes in this case
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#Try to get an object from default instances of the
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#operators...if this fails, return the class
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try:
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op_instances = [op() for op in ops]
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ret = _get_state(op_mapping[ops], set(op_instances), **options)
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except NotImplementedError:
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ret = op_mapping[ops]
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return ret
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else:
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tmp = [type(o) for o in ops]
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classes = frozenset(tmp)
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if classes in op_mapping:
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ret = _get_state(op_mapping[classes], ops, **options)
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else:
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ret = None
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return ret
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else:
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if operators in op_mapping:
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try:
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op_instance = operators()
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ret = _get_state(op_mapping[operators], op_instance, **options)
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except NotImplementedError:
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ret = op_mapping[operators]
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return ret
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elif type(operators) in op_mapping:
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return _get_state(op_mapping[type(operators)], operators, **options)
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else:
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return None
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def state_to_operators(state, **options):
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""" Returns the operator or set of operators corresponding to the
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given eigenstate
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A global function for mapping state classes to their associated
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operators or sets of operators. It takes either a state class
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or instance.
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This function can handle both instances of a given state or just
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the class itself (i.e. both XKet() and XKet)
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There are multiple use cases to consider:
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1) A state class is passed: In this case, we first try
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instantiating a default instance of the class. If this succeeds,
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then we try to call state._state_to_operators on that instance.
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If the creation of the default instance or if the calling of
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_state_to_operators fails, then either an operator class or set of
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operator classes is returned. Otherwise, the appropriate
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operator instances are returned.
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2) A state instance is returned: Here, state._state_to_operators
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is called for the instance. If this fails, then a class or set of
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operator classes is returned. Otherwise, the instances are returned.
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In either case, if the state's class does not exist in
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state_mapping, None is returned.
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Parameters
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==========
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arg: StateBase class or instance (or subclasses)
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The class or instance of the state to be mapped to an
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operator or set of operators
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Examples
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========
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>>> from sympy.physics.quantum.cartesian import XKet, PxKet, XBra, PxBra
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>>> from sympy.physics.quantum.operatorset import state_to_operators
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>>> from sympy.physics.quantum.state import Ket, Bra
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>>> state_to_operators(XKet)
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X
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>>> state_to_operators(XKet())
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X
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>>> state_to_operators(PxKet)
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Px
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>>> state_to_operators(PxKet())
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Px
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>>> state_to_operators(PxBra)
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Px
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>>> state_to_operators(XBra)
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X
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>>> state_to_operators(Ket)
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O
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>>> state_to_operators(Bra)
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O
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"""
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if not (isinstance(state, StateBase) or issubclass(state, StateBase)):
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raise NotImplementedError("Argument is not a state!")
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if state in state_mapping: # state is a class
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state_inst = _make_default(state)
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try:
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ret = _get_ops(state_inst,
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_make_set(state_mapping[state]), **options)
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except (NotImplementedError, TypeError):
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ret = state_mapping[state]
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elif type(state) in state_mapping:
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ret = _get_ops(state,
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_make_set(state_mapping[type(state)]), **options)
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elif isinstance(state, BraBase) and state.dual_class() in state_mapping:
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ret = _get_ops(state,
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_make_set(state_mapping[state.dual_class()]))
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elif issubclass(state, BraBase) and state.dual_class() in state_mapping:
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state_inst = _make_default(state)
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try:
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ret = _get_ops(state_inst,
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_make_set(state_mapping[state.dual_class()]))
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except (NotImplementedError, TypeError):
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ret = state_mapping[state.dual_class()]
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else:
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ret = None
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return _make_set(ret)
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def _make_default(expr):
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# XXX: Catching TypeError like this is a bad way of distinguishing between
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# classes and instances. The logic using this function should be rewritten
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# somehow.
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try:
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ret = expr()
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except TypeError:
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ret = expr
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return ret
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def _get_state(state_class, ops, **options):
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# Try to get a state instance from the operator INSTANCES.
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# If this fails, get the class
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try:
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ret = state_class._operators_to_state(ops, **options)
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except NotImplementedError:
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ret = _make_default(state_class)
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return ret
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def _get_ops(state_inst, op_classes, **options):
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# Try to get operator instances from the state INSTANCE.
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# If this fails, just return the classes
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try:
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ret = state_inst._state_to_operators(op_classes, **options)
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except NotImplementedError:
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if isinstance(op_classes, (set, tuple, frozenset)):
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ret = tuple(_make_default(x) for x in op_classes)
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else:
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ret = _make_default(op_classes)
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if isinstance(ret, set) and len(ret) == 1:
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return ret[0]
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return ret
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def _make_set(ops):
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if isinstance(ops, (tuple, list, frozenset)):
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return set(ops)
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else:
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return ops
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