Related papers: Functional integral with $\phi^4$ term in the acti…
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…
In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…
We present an elementary method of explicit calculation of Young measures for certain class of functions. This class contains in particular functions of a highly oscillatory nature which appear in optimization problems and homogenization…
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…
This paper deals with the numerical integration of Hamiltonian systems in which a stiff anharmonic potential causes highly oscillatory solution behavior with solution-dependent frequencies. The impulse method, which uses micro- and…
In this work, we implement a relatively new analytical technique, the Improved Amplitude-Frequency Formulation (IAFF) method, approach for solving accurate approximate analytical solutions for strong nonlinear oscillators, which may contain…
We propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our…
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,…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
In this work we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal…
This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction…
Computing functional determinants of differential operators is central to any field-theoretical calculation relying on a saddle-point expansion. A variety of approaches is available for the computation that avoid having to know the…
A general technique is developed for calculating functional determinants of second-order differential operators with Dirichlet, periodic, and antiperiodic boundary conditions. As an example, we give simple formulas for a harmonic oscillator…
From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian we extend the functional equation for the Riemann zeta function and develop integral representations for the Riemann xi function that is the completed classical…
We show that certain iteration systems lead to fractal measures admitting exact orthogonal harmonic analysis.
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
We study the Wigner Function in non-commutative quantum mechanics. By solving the time independent Schr\"{o}dinger equation both on a non-commutative (NC) space and a non-commutative phase space, we obtain the Wigner Function for the…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
The spectral theory on the S-spectrum was introduced to give an appropriate mathematical setting to quaternionic quantum mechanics, but it was soon realized that there were different applications of this theory, for example, to fractional…
Our recent method to calculate renormalized functional determinants, the partial wave cutoff method, is extended for the evaluation of 4-D fermion one-loop effective action with arbitrary mass in certain types of radially symmetric,…