Related papers: Coherent States for Unusual Potentials
We formulate a relation between quantum-mechanical coherent states and complex-differentiable structures on the classical phase space ${\cal C}$ of a finite number of degrees of freedom. Locally-defined coherent states parametrised by the…
Logical propositions with the fuzzy modality "Probably" are shown to obey an uncertainty principle very similar to that of Quantum Optics. In the case of such propositions, the partial truth values are in fact probabilities. The…
A common objective for quantum control is to force a quantum system, initially in an unknown state, into a particular target subspace. We show that if the subspace is required to be a decoherence-free subspace of dimension greater than 1,…
In this work we study the effective potential in noncommutative three-dimensional models where the noncommutativity is introduced through the coherent state approach. We discuss some important characteristics that seem to be typical to this…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…
We revisit the problem of quantum tunneling for a particle moving in the continuum, and in the absence of a magnetic field. In all spatial dimensions, we extend previous results to the case where the single-well potential satisfies…
The supersymmetrical approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
Structural models with no solution are incoherent, and those with multiple solutions are incomplete. We show that models with occasionally binding constraints are not generically coherent. Coherency requires restrictions on the parameters…
This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty (and even more, that there are kinds of uncertainty which are for principled reasons not addressable with probabilistic means);…
Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by…
The uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The situation is different if one can build a…
The state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of…
An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like…
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…
We build coherent states (CS) for unbounded motions along two different procedures. In the first one we adapt the Malkin-Manko construction for quadratic Hamiltonians to the motion of a particle in a linear potential. A generalization to…
We generalize the formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates. The generalization is technically almost straightforward…
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one…
Quantum tunneling of the ground and first excited states in a quantum superposition driven by a novel analytical configuration of a double-well (DW) potential is investigated. Symmetric and asymmetric potentials are considered as to support…