Related papers: Green's Function for the Quartic Oscillator
By using the generating function formula for the product of two q-Hermite polynomials q-deformation of the Feynman Green function for the harmonic oscillator is obtained.
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…
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,…
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…
Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
We consider the free space Helmholtz Green's function and split it into the sum of oscillatory and non-oscillatory (singular) components. The goal is to separate the impact of the singularity of the real part at the origin from the…
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…
We find that correlation functions at one dimension are crucially affected by the curvature of the bare single particle spectrum. Parabolic curvature leads to two closely related phenomena: the Green's function exhibits oscillation (as a…
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…
We show that the Green's functions in non-linear gauge in the theory of perturbative quantum gravity is expressed as a series in terms of those in linear gauges. This formulation is also holds for operator Green's functions. We further…
Gauge invariant quark two-point Green's functions defined with path-ordered gluon field phase factors along skew-polygonal lines joining the quark to the antiquark are considered. Functional relations between Green's functions with…
We consider gauge invariant quark two-point Green's functions in which the gluonic phase factor follows a skew-polygonal line. Using a particular representation for the quark propagator in the presence of an external gluon field, functional…
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…
A new scheme has been proposed to solve the B.E. condenstates in terms of Green's function approach. It has been shown that the radial wave function of two interacting atoms, moving in a common harmonic oscillator potential modified by an…
The Green's function formalism for neutrino mixing is presented and the exact oscillation formula is obtained. The usual Pontecorvo formula is recovered in the relativistic limit.
We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schroedinger equation with variable quadratic Hamiltonians. The Green…
In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics ($\mathbbm{H}$QM) in the real Hilbert space, both in the analytic method and in the algebraic method. The quaternionic solutions have many…
We introduce a hybrid quantum-classical algorithm to compute the Green function for strongly correlated electrons on noisy intermediate-scale quantum (NISQ) devices. The technique consists in the construction of a non-orthogonal excitation…
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…