Related papers: A coherent state associated with shape-invariant p…
In the theory of Toeplitz quantization of algebras, as developed by the second author, coherent states are defined as eigenvectors of a Toeplitz annihilation operator. These coherent states are studied in the case when the algebra is the…
The Heisenberg algebra is deformed with the set of parameters ${q, l,\lambda}$ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly…
In this paper, we show that an attempt to construct shape invariant extensions of a known shape invariant potential leads to, apart from a shift by a constant, the well known technique of isospectral shift deformation. Using this, we…
The distribution of eigenvalues of the wave equation in a bounded domain is known as Weyl's problem. We describe several computational projects related to the cumulative state number, defined as the number of states having wavenumber up to…
One of the most important issues of quantum engineering is the construction of low-dimensional structures possessing desirable properties. For example, in different areas of possible applications of the structures containing quantum wells…
A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for…
Known shape-invariant potentials for the constant-mass Schrodinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance condition turns out to be deformed. Its…
We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on a Hilbert space. As applications, we characterize compactness of affine and Weyl-Heisenberg localization operators as well as…
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols and…
This contribution to the present Workshop Proceedings outlines a general programme for identifying geometric structures--out of which to possibly recover quantum dynamics as well--associated to the manifold in Hilbert space of the quantum…
In this work, we consider the propagation of acoustic waves in unbounded domains characterized by a constant wavenumber, except possibly in a bounded region. The geometry of this inhomogeneity is assumed to be uncertain, and we are…
The support of wavelet transform associated with square integrable irreducible representation of a homogeneous space is shown to have infinite measure. Pointwise homogeneous approximation property for wavelet transform has been…
In this work we present a semi-classical approach to solve the inverse spectrum problem for one-dimensional wave equations for a specific class of potentials that admits quasi-stationary states. We show how inverse methods for potential…
In quantum mechanics with minimal length uncertainty relations the Heisenberg-Weyl algebra of the one-dimensional harmonic oscillator is a deformed SU(1,1) algebra. The eigenvalues and eigenstates are constructed algebraically and they form…
String-localized quantum field theory allows renormalizable couplings involving massive vector bosons, without invoking negative-norm states and compensating ghosts. We analyze the most general coupling of a massive vector boson to a scalar…
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the distant variable is restricted from one side, . By this reason…
The hypergeometric type operators are shape invariant, and a factorization into a product of first order differential operators can be explicitly described in the general case. Some additional shape invariant operators depending on several…
A general procedure for constructing coherent states, which are eigenstates of annihilation operators, related to quantum mechanical potential problems, is presented. These coherent states, by construction are not potential specific and…
We show that the conditional shape invariance symmetry can be used as a very powerful tool to calculate the eigenvalues of the mixed potential V (r) = ar + br^2 +c/r + l(l+1)/r^2 for a restricted set of potential parameters. The energy for…