相关论文: A q-oscillator Green Function

The q-special functions appear naturally in q-deformed quantum mechanics and both sides profit from this fact. Here we study the relation between the q-deformed harmonic oscillator and the q-Hermite polynomials. We discuss: recursion…

We compute the ($q_1,q_2$)-deformed Hermite polynomials by replacing the quantum harmonic oscillator problem to Fibonacci oscillators. We do this by applying the ($q_1, q_2$)-extension of Jackson derivative. The deformed energy spectrum is…

By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of…

In this paper, a quantum mechanical Green's function $G_{qo}(y_b,t_b;$ $y_a,t_a)$ for the quartic oscillator is presented. This result is built upon two previous papers: first [1], detailing the linearization of the quartic oscillator…

We compute the partition function of an anyon-like harmonic oscillator. The well known results for both the bosonic and fermionic oscillators are then reobtained as particular cases as ours. The technique we employ is a non-relativistic…

We use generating functions to express orthogonality relations in the form of $q$-beta integrals. The integrand of such a $q$-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal

Different generators of a deformed oscillator algebra give rise to one-parameter families of $q$-exponential functions and $q$-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment…

One more model of a q-harmonic oscillator based on the q-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier…

It has been shown that the Schwinger-Dyson equations for non-Hermitian theories implicitly include the Hilbert-space metric. Approximate Green functions for such theories may thus be obtained, without having to evaluate the metric…

A new approach proposed recently by author for the calculation of Green functions in quantum field theory and quantum mechanics is briefly reviewed. The method is applied to nonperturbative calculations for anharmonic oscillator,…

We construct Green's function for the quantum degenerate parametric oscillator in terms of standard solutions of Ince's equation in a framework of a general approach to harmonic oscillators. Exact time-dependent wave functions and their…

Homogeneous and inhomogeneous biharmonic equation are considered on the $n$-dimensional unit sphere. The Green function is given as a series of Gegenbauer polynomials. In the paper, explicit representations of the Green function are found…

The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…

The Green's function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of Green's function impedes the research of…

In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…

From the realization of $q-$oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szeg\H{o} polynomials as well as…

The q-deformed harmonic oscillator is studied in the light of q-deformed phase space variables. This allows a formulation of the corresponding Hamiltonian in terms of the ordinary canonical variables $x$ and $p$. The spectrum shows…

The one-dimensional time-independent Green's function $G_0$ of a quantum simple harmonic oscillator system ($V_0(x)=m \omega^2 x^2/2$) can be obtained by solving the equation directly. It has a compact expression, which gives correct…

Green function (which can be called the q-analogous of the Hankel function) on the quantum plane E_q^2= E_q(2)/U(1) is constructed.

A model of a q-harmonic oscillator based on q-Charlier polynomials of Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation…