a khL@sdZddlmZddlmZddlmZddlmZm Z ddl m Z ddl m Z ddlmZdd lmZdd lmZdd lmZdd lmZmZdd lmZddlmZgdZGdddeZGdddeZGdddeZ GdddeZ!GdddeZ"GdddeZ#dS)aQuantum mechanical operators. TODO: * Fix early 0 in apply_operators. * Debug and test apply_operators. * Get cse working with classes in this file. * Doctests and documentation of special methods for InnerProduct, Commutator, AntiCommutator, represent, apply_operators. )Optional)Add)Expr) Derivativeexpand)MulooS prettyForm)Dagger) OperatorKind)QExprdispatch_method)eye)sympy_deprecation_warning)OperatorHermitianOperatorUnitaryOperatorIdentityOperator OuterProductDifferentialOperatorc@seZdZUdZdZeeed<dZeeed<e ddZ e Z dZ dd ZeZd d Zd d ZddZddZddZddZddZddZddZddZeZddZdS) ra Base class for non-commuting quantum operators. An operator maps between quantum states [1]_. In quantum mechanics, observables (including, but not limited to, measured physical values) are represented as Hermitian operators [2]_. Parameters ========== args : tuple The list of numbers or parameters that uniquely specify the operator. For time-dependent operators, this will include the time. Examples ======== Create an operator and examine its attributes:: >>> from sympy.physics.quantum import Operator >>> from sympy import I >>> A = Operator('A') >>> A A >>> A.hilbert_space H >>> A.label (A,) >>> A.is_commutative False Create another operator and do some arithmetic operations:: >>> B = Operator('B') >>> C = 2*A*A + I*B >>> C 2*A**2 + I*B Operators do not commute:: >>> A.is_commutative False >>> B.is_commutative False >>> A*B == B*A False Polymonials of operators respect the commutation properties:: >>> e = (A+B)**3 >>> e.expand() A*B*A + A*B**2 + A**2*B + A**3 + B*A*B + B*A**2 + B**2*A + B**3 Operator inverses are handle symbolically:: >>> A.inv() A**(-1) >>> A*A.inv() 1 References ========== .. [1] https://en.wikipedia.org/wiki/Operator_%28physics%29 .. [2] https://en.wikipedia.org/wiki/Observable N is_hermitian is_unitarycCsdS)N)OselfrrL/var/www/auris/lib/python3.9/site-packages/sympy/physics/quantum/operator.py default_argsnszOperator.default_args,cGs|jjSN) __class____name__rprinterargsrrr _print_operator_namezszOperator._print_operator_namecGs t|jjSr#)r r$r%r&rrr _print_operator_name_prettysz$Operator._print_operator_name_prettycGsLt|jdkr |j|g|RSd|j|g|R|j|g|RfSdS)N%s(%s))lenlabel _print_labelr)r&rrr _print_contentss zOperator._print_contentscGslt|jdkr |j|g|RS|j|g|R}|j|g|R}t|jddd}t||}|SdS)Nr+()leftright)r-r._print_label_prettyr*r parensr5rr'r(pformZ label_pformrrr _print_contents_prettys zOperator._print_contents_prettycGsLt|jdkr |j|g|RSd|j|g|R|j|g|RfSdS)Nr+z%s\left(%s\right))r-r.Z_print_label_latex_print_operator_name_latexr&rrr _print_contents_latexs zOperator._print_contents_latexcKst|d|fi|S)z:Evaluate [self, other] if known, return None if not known._eval_commutatorrrotheroptionsrrr r=szOperator._eval_commutatorcKst|d|fi|S)z Evaluate [self, other] if known._eval_anticommutatorr>r?rrr rBszOperator._eval_anticommutatorcKst|d|fi|S)N_apply_operatorr>rketrArrr rCszOperator._apply_operatorcKsdSr#rrbrarArrr _apply_from_right_toszOperator._apply_from_right_tocGs tddS)Nzmatrix_elements is not defined)NotImplementedError)rr(rrr matrix_elementszOperator.matrix_elementcCs|Sr# _eval_inverserrrr inverseszOperator.inversecCs|dSNrrrrr rLszOperator._eval_inverse)r% __module__ __qualname____doc__rrbool__annotations__r classmethodr!rkindZ_label_separatorr)r;r*r0r:r<r=rBrCrHrJrMinvrLrrrr r*s* A    rc@s$eZdZdZdZddZddZdS)raA Hermitian operator that satisfies H == Dagger(H). Parameters ========== args : tuple The list of numbers or parameters that uniquely specify the operator. For time-dependent operators, this will include the time. Examples ======== >>> from sympy.physics.quantum import Dagger, HermitianOperator >>> H = HermitianOperator('H') >>> Dagger(H) H TcCst|tr|St|SdSr#) isinstancerrrLrrrr rLs zHermitianOperator._eval_inversecCs8t|tr,|jr"ddlm}|jS|jr,|St||S)Nrr ) rXrZis_evensympy.core.singletonr ZOneZis_oddr _eval_power)rexpr rrr rZs  zHermitianOperator._eval_powerN)r%rPrQrRrrLrZrrrr rsrc@seZdZdZdZddZdS)raA unitary operator that satisfies U*Dagger(U) == 1. Parameters ========== args : tuple The list of numbers or parameters that uniquely specify the operator. For time-dependent operators, this will include the time. Examples ======== >>> from sympy.physics.quantum import Dagger, UnitaryOperator >>> U = UnitaryOperator('U') >>> U*Dagger(U) 1 TcCs|Sr#rKrrrr _eval_adjointszUnitaryOperator._eval_adjointN)r%rPrQrRrr\rrrr rsrc@seZdZdZdZdZeddZeddZ ddZ d d Z d d Z d dZ ddZddZddZddZddZddZddZddZdS) ra,An identity operator I that satisfies op * I == I * op == op for any operator op. .. deprecated:: 1.14. Use the scalar S.One instead as the multiplicative identity for operators and states. Parameters ========== N : Integer Optional parameter that specifies the dimension of the Hilbert space of operator. This is used when generating a matrix representation. Examples ======== >>> from sympy.physics.quantum import IdentityOperator >>> IdentityOperator() # doctest: +SKIP I TcCs|jSr#)Nrrrr dimensionszIdentityOperator.dimensioncCstfSr#rrrrr r!szIdentityOperator.default_argscOsLtddddt|dvr&td|t|dkrB|drB|dnt|_dS) Nz IdentityOperator has been deprecated. In the future, please use S.One as the identity for quantum operators and states. z1.14zdeprecated-operator-identity)Zdeprecated_since_versionZactive_deprecations_target)rr+z"0 or 1 parameters expected, got %sr+r)rr- ValueErrorr r])rr(hintsrrr __init__ s  zIdentityOperator.__init__cKstjSr#)r ZZerorr@r`rrr r=.sz!IdentityOperator._eval_commutatorcKsd|S)Nrrbrrr rB1sz%IdentityOperator._eval_anticommutatorcCs|Sr#rrrrr rL4szIdentityOperator._eval_inversecCs|Sr#rrrrr r\7szIdentityOperator._eval_adjointcKs|Sr#rrDrrr rC:sz IdentityOperator._apply_operatorcKs|Sr#rrFrrr rH=sz%IdentityOperator._apply_from_right_tocCs|Sr#r)rr[rrr rZ@szIdentityOperator._eval_powercGsdSNIrr&rrr r0Csz IdentityOperator._print_contentscGstdSrdr r&rrr r:Fsz'IdentityOperator._print_contents_prettycGsdS)Nz {\mathcal{I}}rr&rrr r<Isz&IdentityOperator._print_contents_latexcKsF|jr|jtkrtd|dd}|dkr>> from sympy.physics.quantum import Ket, Bra, OuterProduct, Dagger >>> k = Ket('k') >>> b = Bra('b') >>> op = OuterProduct(k, b) >>> op |k>>> op.hilbert_space H >>> op.ket |k> >>> op.bra >> Dagger(op) |b>>> k*b |k>>> b*k*b *>> from sympy import Derivative, Function, Symbol >>> from sympy.physics.quantum.operator import DifferentialOperator >>> from sympy.physics.quantum.state import Wavefunction >>> from sympy.physics.quantum.qapply import qapply >>> f = Function('f') >>> x = Symbol('x') >>> d = DifferentialOperator(1/x*Derivative(f(x), x), f(x)) >>> w = Wavefunction(x**2, x) >>> d.function f(x) >>> d.variables (x,) >>> qapply(d*w) Wavefunction(2, x) cCs |jdjS)a Returns the variables with which the function in the specified arbitrary expression is evaluated Examples ======== >>> from sympy.physics.quantum.operator import DifferentialOperator >>> from sympy import Symbol, Function, Derivative >>> x = Symbol('x') >>> f = Function('f') >>> d = DifferentialOperator(1/x*Derivative(f(x), x), f(x)) >>> d.variables (x,) >>> y = Symbol('y') >>> d = DifferentialOperator(Derivative(f(x, y), x) + ... Derivative(f(x, y), y), f(x, y)) >>> d.variables (x, y) rOrrrrrr variablesszDifferentialOperator.variablescCs |jdS)ad Returns the function which is to be replaced with the Wavefunction Examples ======== >>> from sympy.physics.quantum.operator import DifferentialOperator >>> from sympy import Function, Symbol, Derivative >>> x = Symbol('x') >>> f = Function('f') >>> d = DifferentialOperator(Derivative(f(x), x), f(x)) >>> d.function f(x) >>> y = Symbol('y') >>> d = DifferentialOperator(Derivative(f(x, y), x) + ... Derivative(f(x, y), y), f(x, y)) >>> d.function f(x, y) rOrrrrrr function4szDifferentialOperator.functioncCs |jdS)a Returns the arbitrary expression which is to have the Wavefunction substituted into it Examples ======== >>> from sympy.physics.quantum.operator import DifferentialOperator >>> from sympy import Function, Symbol, Derivative >>> x = Symbol('x') >>> f = Function('f') >>> d = DifferentialOperator(Derivative(f(x), x), f(x)) >>> d.expr Derivative(f(x), x) >>> y = Symbol('y') >>> d = DifferentialOperator(Derivative(f(x, y), x) + ... Derivative(f(x, y), y), f(x, y)) >>> d.expr Derivative(f(x, y), x) + Derivative(f(x, y), y) rrrrrrr exprLszDifferentialOperator.exprcCs|jjS)z< Return the free symbols of the expression. )r free_symbolsrrrr resz!DifferentialOperator.free_symbolscKsPddlm}|j}|jdd}|j}|j|||}|}||g|RS)Nr) Wavefunctionr+)rlrr~r(rrsubsZdoit)rfuncrArvarZwf_varsfnew_exprrrr _apply_operator_Wavefunctionms z1DifferentialOperator._apply_operator_WavefunctioncCst|j|}t||jdSrN)rrrr()rsymbolrrrr _eval_derivativexs z%DifferentialOperator._eval_derivativecGs(d|j|g|R|j|g|RfS)Nr,)r)r/r&rrr rtszDifferentialOperator._printcGsH|j|g|R}|j|g|R}t|jddd}t||}|S)Nr1r2r3)r*r6r r7r5r8rrr _print_prettys z"DifferentialOperator._print_prettyN) r%rPrQrRrir~rrrrrrtrrrrr rs)     rN)$rRtypingrZsympy.core.addrZsympy.core.exprrZsympy.core.functionrrZsympy.core.mulrZsympy.core.numbersr rYr Z sympy.printing.pretty.stringpictr Zsympy.physics.quantum.daggerrZsympy.physics.quantum.kindrZsympy.physics.quantum.qexprrrZsympy.matricesrZsympy.utilities.exceptionsr__all__rrrrrrrrrr s,           'Y