Related papers: A simplified approach to the improved semiclassica…
Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasi-exactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
A simple criterion is derived in order that a number sequence ${\cal S}_n$ is a permitted spectrum of a quantized system. The sequence of the prime numbers fulfils the criterion and the corresponding one-dimensional quantum potential is…
A new algorithm for estimating the fraction of numbers that is present in a superpositional state which satisfies a given condition,is introduced.This algorithm is conceptually simple and does not require quantum Fourier transform.Also the…
The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB…
Under categorial grammars that have powerful rules like composition, a simple n-word sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This…
We address the problem of incremental sequence classification, where predictions are updated as new elements in the sequence are revealed. Drawing on temporal-difference learning from reinforcement learning, we identify a…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for…
A sixth order quadrupole boson Hamiltonian is treated through a time dependent variational principle approach choosing as trial function a coherent state with respect to zeroth $b^{\dagger}_0$ and second $b^{\dagger}_2+b^{\dagger}_{-2}$…
It is shown here how the semiclassical theory of electrical susceptibility can be extended to the case in which both radiation and matter are quantized. This is done specifically for the cases of linear and second order susceptibilities.…
We discuss the (re-)construction of quasiprobability representations from generic measurements, including noisy ones. Based on the measurement under study, quasiprobabilities and the associated concept of nonclassicality are introduced. A…
Algebraic quantization scheme has been proposed as an extension of the Dirac quantization scheme for constrained systems. Semi-classical states for constrained systems is also an independent and important issue, particularly in the context…
Term algebras are important objects in computer science and are correspondingly well-studied. A natural generalization is to quotient these algebras by finitely many ground term equations, obtaining what we call almost free algebras. One of…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
Quantifier elimination of positive semidefinite cyclic ternary quartic forms is studied in this paper. We solve the problem by the theory of complete discrimination systems, function \RealTriangularize in Maple15 and the so-called…
In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional,…
We describe a systematic expansion for full QCD. The leading term in the expansion gives the valence approximation. The expansion reproduces full QCD if an infinite number of higher terms are included.
We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the…
We derive semiclassical quantization conditions for systems with spin. To this end one has to define the notion of integrability for the corresponding classical system which is given by a combination of the translational motion and…