相关论文: Generalized Binomial States: Ladder Operator Appro…
We propose a ladder-operator method for obtaining the squeezed states of general symmetry systems. It is a generalization of the annihilation-operator technique for obtaining the coherent states of symmetry systems. We connect this method…
Both the coherent states and also the squeezed states of the harmonic oscillator have long been understood from the three classical points of view: the 1) displacement operator, 2) annihilation- (or ladder-) operator, and…
In this paper we consider squares of pseudo-bosonic ladder operators and we use them to produce explicit examples of eigenstates of certain operators satisfying a deformed $\mathfrak{su}(1,1)$ Lie algebra. We show how these eigenstates may,…
A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the…
We propose a displacement-operator approach to some aspects of squeezed states for general multiphoton systems. The explicit displacement-operators of the squeezed vacuum and the coherent states are achieved and expresses as the ordinary…
In this note we generalize the Ball-James rigidity theorem for gradient differential inclusions to the setting of a general linear differential constraint. In particular, we prove the rigidity for approximate solutions to the two-state…
We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well…
As an aid to understanding the {\it displacement operator} definition of squeezed states for arbitrary systems, we investigate the properties of systems where there is a Holstein-Primakoff or Bogoliubov transformation. In these cases the…
In this article a study was made of the conditions under which a Hamiltonian which is an element of the complex $ \left\{ h (1) \oplus h(1) \right\} \uplus u(2) $ Lie algebra admits ladder operators which are also elements of this algebra.…
High-order methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is provided by summation-by-parts (SBP) operators and the weak enforcement of…
In this paper, we construct corrections to the raising and lowering (i.e. ladder) operators for a quantum harmonic oscillator subjected to a polynomial type perturbation of any degree and to any order in perturbation theory. We apply our…
Gaussian boson sampling (GBS) is considered a candidate problem for demonstrating quantum advantage. We propose an algorithm for approximate classical simulation of a lossy GBS instance. The algorithm relies on the Taylor series expansion,…
The supersymmetry in quantum mechanics and shape invariance condition are applied as an algebraic method to solve the Dirac-Coulomb problem. The ground state and the excited states are investigated using new generalized ladder operators.
The constraint operators belonging to a generally covariant system are found out within the framework of the BRST formalism. The result embraces quadratic Hamiltonian constraints whose potential can be factorized as a never null function…
We show that various kinds of one-photon quantum states studied in the field of quantum optics admit ladder operator formalisms and have the generally deformed oscillator algebraic structure. The two-photon case is also considered. We…
The eigenvalues of the complete commuting set of self-adjoint operators determine the classification of states. We construct a classification for the image of the Jordan-Schwinger mapping of the su(2) algebra. We use the ladder operator…
We extend the definition of generalized coherent states to include the case of time-dependent dispersion. We introduce a suitable operator providing displacement and dynamical rescaling from an arbitrary ground state. As a consequence,…
The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a scalar theory: two scalar fields (constituents) with mass $m$ interacting via an exchange of a scalar field (tieon) with mass $\mu$. The BS equation is written…
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the…
In this paper the factorization method is used in order to obtain the eigenvalues and eigenfunctions of a quantum particle confined in a one-dimensional infinite well. The output results from the mentioned approach allows us to explore an…