Related papers: Higher power squeezed states, Jacobi matrices, and…
We study the eigenvalue problem for a linear potential Hamiltonian and, by writing Airy equation in terms of momentum and position operators define Airy states. We give a solution of the Schr\"odinger equation for the symmetrical linear…
In this paper we use the Lie algebra of space-time symmetries to construct states which are solutions to the time-dependent Schr\"odinger equation for systems with potentials $V(x,\tau)=g^{(2)}(\tau)x^2+g^{(1)}(\tau)x +g^{(0)}(\tau)$. We…
We consider the class of non-Hermitian operators represented by infinite tridiagonal matrices, selfadjoint in an indefinite inner product space with one negative square. We approximate them with their finite truncations. Both infinite and…
Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt…
We address facts and open questions concerning the degree of ill-posedness of the composite Hausdorff moment problem aimed at the recovery of a function $x \in L^2(0,1)$ from elements of the infinite dimensional sequence space $\ell^2$ that…
By the complex multimode Bogoliubov transformation, we obtain the general forms of squeeze operators and squeezed states including squeezed vacuum states, squeezed coherent states, squeezed Fock states and squeezed coherent Fock states, for…
With the help of a useful mathematical tool, the polar decomposition of closed operators, and a simple observation, i.e. the unique relation between tensor-product states and compact operators, we manage to give a compact and coherent…
Beam splitters are routinely used for generating entanglement between modes in the optical and microwave domains, requiring input states that are not convex combinations of coherent states. This leads to the ability to generate entanglement…
In this paper, subnormal operators, not necessarily bounded, are discussed as generalized observables. In order to describe not only the information about the probability distribution of the output data of their measurement but also a…
We consider the Jacobi operator (T,D(T)) associated with an indeterminate Hamburger moment problem, and present countable subsets S of the domain D(T) such that span(S) is dense in \ell^2. As an example we have…
By means of numerical solutions of the quantum Hamilton Jacobi equation, a general WKB-like representation for one-dimensional wave functions is obtained. This representation is unique in the classically forbidden regions, while in the…
We prove necessary and sufficient conditions for the Schr\"odinger operators to have zero-energy bound states at the threshold of the essential spectrum such that they have bounded $k$-th moment. This result is the extension of the results…
This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schr\"odinger equation with invariant evolution parameter, and…
This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements $\rho(z',z)$, derivedfrom $(q;l,\lambda)-$deformed boson coherent states.The induced $\rho(z',z)$ self-reproducing property…
We use classical results from the theory of linear preserver problems to characterize operators that send the set of pure states with Schmidt rank no greater than k back into itself, extending known results characterizing operators that…
The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more…
Fan-even K-quantum nonlinear coherent states are introduced and higher-order amplitude squeezing is investigated in such states. It is shown that for a given K the lowest order in which an amplitude component can be squeezed is 2K and the…
Two new types of coherent states associated with the C_{\lambda}-extended oscillator, where C_{\lambda} is the cyclic group of order \lambda, are introduced. The first ones include as special cases both the Barut-Girardello and the…
A new, coercive formulation of the Helmholtz equation was introduced in [Moiola, Spence, SIAM Rev. 2014]. In this paper we investigate $h$-version Galerkin discretisations of this formulation, and the iterative solution of the resulting…
The multi-qubit GHZ state possesses tangles with elegant transformation properties under stochastic local operations and classical communication. Since almost all pure 3-qubit states are connected to the GHZ state via SLOCC, we derive a…