Operator/State Helper Functions#

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

sympy.physics.quantum.operatorset.operators_to_state(operators, **options)[source]#

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>

sympy.physics.quantum.operatorset.state_to_operators(state, **options)[source]#

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