COMMUTING operators (Quantum mechanics)LINEAR operatorsPERTURBATION theoryWe present a general counting result for the unstable eigenvalues of linear operators of the form J L in which J and L are skew- and self
the set of operators \(x\in {{\mathcal {A}}}\) with \(0\le x\le 1\), is denoted \([0,1]_{{\mathcal {A}}}\). The algebra of bounded operators on a Hilbert space \(\mathcal {H}\) is denoted \({{\mathcal {B}}}(\mathcal {H})\), and the identity operator is ...
There is a constant threshold th such that if ‖Nj − output of the noisy commuting quantum circuits is impossible denotes the diamond norm of the super-operators42. I‖◊ ≤εth, then efficient classical simulation of unless the PH collapses at the third level. Here ‖ the ⋅ ‖...
The problem is also renowned thanks to its connection to physics, originally noticed by von Neumann in his approach to quantum mechanics [20]. The commutator equation being an example, the existence of exactly commuting matrices near almost commuting matrices can be viewed in a wider context of ...
Kato, T. Perturbation Theory for Linear Operators (Springer-Verlag, 1995). Dembowski, C. et al. Experimental observation of the topological structure of exceptional points. Phys. Rev. Lett. 86, 787–790 (2001). Article ADS CAS PubMed Google Scholar Arnold, V. I. On matrices depending on...
COMMUTING operators (Quantum mechanics)PROBABILITY theoryMATHEMATICAL analysisRING theoryMATHEMATICSANALYTIC geometryIn this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself is equal to a ...
In this chapter we will study a central theorem (Theorem 15.1) concerning a pair of commuting self-adjoint operators, that is, those representing observables in the formalism of quantum mechanics. This theorem is of fundamental importance in quantum theory, and, as we shall see, leads to the...
Two particle quantum mechanics in 2+1 Gravity using non commuting coordinates - Welling () Citation Context ...d by a relative distance between two particles. Some progress has been made towards this goal on the level of the classical phase space [19] and a simple model has been worked ...
This way the self-adjoint operatorf(aA+bB)can be computed out of the PVMs of the self-adjoint operatorsAandB. Equation (2) is valid for generally non-commutingP^{(A)}andP^{(B)}, also in the case of unbounded self-adjoint operatorsAandBunder the condition thataA+bBis essentially self...
angular momentum operatorsdistribution functionsquantum mechanicsprobabilityspinbohm criterionatomic modelscommutation relationseigenvaluesWe use joint probabilities to analyze the EPR argument in the Bohm's example of spins. (1) The properties of distribution functions for two, three, or more noncommuting ...