相关论文: Complementarity and the uncertainty relations
Heisenberg's uncertainty relation for measurement noise and disturbance states that any position measurement with noise epsilon brings the momentum disturbance not less than hbar/2epsilon. This relation holds only for restricted class of…
In this work, we show that the completeness relation for the eigenvectors, which is an essential assumption of quantum mechanics, remains true if the Hamiltonian, having a discrete spectrum, is modified by a delta potential (to be made…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The significance of this "exact"…
A coherent account of the connections and contrasts between the principles of com- plementarity and uncertainty is developed starting from a survey of the various formalizations of these principles. The conceptual analysis is illustrated by…
A model of the Einstein-Bohr double-slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has the double slits in it, as well as the state of a particle incoming…
An overview of the conceptuality interpretation of quantum mechanics is presented, along with an explanation of how it sheds light on key quantum and relativistic phenomena. In particular, we show how the interpretation clarifies…
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general dificulty in the formation of human ideas, inherent…
Extended quantum mechanics using non-Hermitian, pseudo-Hermitian Hamiltonians is briefly reviewed. Supersymmetric regularizations, solvable simulations and large-N expansion techniques are recollected as suitable means for the study of…
It has been shown that inclusion of higher order curvature invariant terms in the Robertson-Walker minisuperspace model of the Einstein-Hilbert action leads to Schrodinger like equation, whose corresponding effective action is hermitian.…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
Some PT-symmetric non-hermitean Hamiltonians have only real eigenvalues. There is numerical evidence that the associated PT-invariant energy eigenstates satisfy an unconventional completeness relation. An ad hoc scalar product among the…
Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
We introduce a complete set of complementary quantities in bipartite, two-dimensional systems. Complementarity then relates the quantitative entanglement measure concurrence which is a bipartite property to the single-particle quantum…
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=\omega^{ij}(x), and construct the complete algebra of…
A correspondence of classical to quantum physics studied by Schr\"{o}\-dinger and Ehrenfest applies without the necessity of technical conjecture that classical observables are associated with Hermitian Hilbert space operators. This…
Quantum coherence and quantum correlations lie in the center of quantum information science, since they both are considered as fundamental reasons for significant features of quantum mechanics different from classical mechanics. We present…
The uncertainty relations (URs) of two arbitrary Hermitian and non-Hermitian incompatible operators represented by the product of variances have been confirmed theoretically and experimentally in various physical systems. However, the lower…