Factorizing the time evolution operator

There is a widespread belief in the quantum physical community, and in textbooks used to teach Quantum Mechanics, that it is a difficult task to apply the time evolution operator Exp{-itH/h} on an initial wave function. That is to say, because the hamiltonian operator generally is the sum of two operators, then it is a difficult task to apply the time evolution operator on an initial wave function f(x,0), for it implies to apply terms operators like (a+b)^n. A possible solution of this problem is to factorize the time evolution operator and then apply successively the individual exponential operator on the initial wave function. However, the exponential operator does not directly factorize, i. e. Exp{a+b} is not equal to Exp{a}Exp{b}. In this work we present a useful procedure for factorizing the time evolution operator when the argument of the exponential is a sum of two operators, which obey specific commutation relations. Then, we apply the exponential operator as an evolution operator for the case of elementary unidimensional potentials, like the particle subject to a constant force and the harmonic oscillator. Also, we argue about an apparent paradox concerning the time evolution operator and non-spreading wave packets addressed previously in the literature.Comment: 24 pages; added references; one figure change

Exact solution of the Schrodinger equation with the spin-boson Hamiltonian

We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (enviroment). An exact solution of the Schrodinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.Comment: 9 pages, LaTeX, to appear in Journal of Physics A: Mathematical and Theoretica

Mixoma odontogénico: caso clínico y revisión de la literatura

El mixoma odontogénico (MO) es una neoplasia intraósea benigna de crecimiento lento localmente agresiva que deriva del tejido mesenquimatoso del germen dentario. Representa del 3 al 20% de todos los tumores odontogénicos. Tiene una predilección por el genero femenino entre la segunda y cuarta década de la vida. Histopatológicamente presenta células ahusadas y estrelladas embebidas en una matriz extracelular mixoide. Radiográficamente presenta varios diagnósticos diferenciales y su tratamiento va desde enucleación y legrado hasta cirugía radical, extirpando tejidos adyacentes.El propósito de este trabajo es presentar el caso clínico de un paciente femenino de 31 años con diagnóstico compatible con mixoma odontogénico localizado en el cuerpo mandibular y rama ascendente derecha