相关论文: On the factorization method in quantum mechanics

We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by…

A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…

Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…

We show that the Dirac factorization method can be successfully employed to treat problems involving operators raised to a fractional power. The technique we adopt is based on an extension of the Pauli matrices and the properties of the…

New families of time-dependent potentials related with the stationary singular oscillator are introduced. This is achieved after noticing that a non stationary quantum invariant can be constructed for the singular oscillator. Such invariant…

A matrix factorization problem is considered. The matrix to be factorized is algebraic, has dimension 2 X 2 and belongs to Moiseev's class. A new method of factorization is proposed. First, the matrix factorization problem is reduced to a…

We apply the factorization technique developed by Kuru and Negro [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric…

Based on the fact that the Hamiltonians of the Coulomb many-particle systems are always factorized we develop the two different approaches for analytical solution of the Schr\"{o}dinger equation written for arbitrary few- and many-particle…

A brief description of the relations between the factorization method in quantum mechanics, self-similar potentials, integrable systems and the theory of special functions is given. New coherent states of the harmonic oscillator related to…

We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure…

We present a quantum electronic embedding method derived from the exact factorization approach to calculate static properties of a many-electron system. The method is exact in principle but the practical power lies in utilizing input from a…

A number of problems in theoretical physics share a common nucleus of combinatoric nature. It is argued here that Hopf algebraic concepts and techiques can be particularly efficient in dealing with such problems. As a first example, a brief…

We generalize effective energy variational techniques to study appropriately quantized solitonic field configurations. Our approach rests on collective quantization ideas and is specifically designed for the numerical evaluation of soliton…

The factorizations using the general Riccati solution constructed from a given particular solution by means of the Bernoulli ansatz initiated in 1984 by Mielnik and Fernandez C. for the cases of the quantum harmonic oscillator and the…

We start with elementary algebraic theory of factorization of linear ordinary differential equations developed in the period 1880-1930. After exposing these classical results we sketch more sophisticated algorithmic approaches developed in…

Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…

In a previous work we showcased the factorization method to find the symmetries of superintegrable systems with spherical separability in flat spaces. Here we analyze the same problem, but in constant curvature spaces along the examples of…

The concept of effective particles is introduced in the Minkowski space-time Hamiltonians in quantum field theory using a new kind of the relativistic renormalization group procedure that does not integrate out high-energy modes but instead…

It is unusual to find QCD factorization explained in the language of quantum information science. However, we will discuss how the issue of factorization and its breaking in high-energy QCD processes relates to phenomena like decoherence…

The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…