Related papers: Anharmonic oscillator and double-well potential: a…
The simplest possible noncommutative harmonic oscillator in two dimensions is used to quantize the free closed bosonic string in two flat dimensions. The partition function is not deformed by the introduction of noncommutativity, if we…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
Classical and quantum anharmonic noncommutative oscillators with quartic self-interacting potential are considered and the effect of self-interaction term on the free energy and partition function of both models is calculated to first order…
One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in…
We consider a polyharmonic operator $H=(-\Delta)^l+V(x)$ in dimension two with $l\geq 6$ and a limit-periodic potential $V(x)$. We prove that the spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at…
We present an oscillator modeling of the relativistic spin-0 charges moving in the quantum states with minimum coupling of electromagnetic fields. Rather than perturbative approach to spinless regime, we put into operation directly under…
The auxiliary field method, defined through introducing an auxiliary (also called as the Hubbard-Stratonovich or the Mean-) field and utilizing a loop-expansion, gives an excellent result for a wide range of a coupling constant. The…
We systematically investigate different versions of variational perturbation theory by forcing not only the first or second but also higher derivatives of the approximant with respect to the variational parameter to vanish. The choice of…
An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The…
We prove an upper bound proportional to the surface area for the bipartite entanglement of the ground state and thermal states of harmonic oscillator systems with disorder, as measured by the logarithmic negativity. Our assumptions are…
We study solutions of the functional eigenstate equation of a free quantum field Hamiltonian. Admissible solutions are to have a finite norm and a finite eigenvalue w.r.t. the norm and eigenvalue of the ground state of the free theory. We…
We introduce an orbital free electron density functional approximation based on alchemical perturbation theory. Given convergent perturbations of a suitable reference system, the accuracy of popular self-consistent Kohn-Sham density…
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,…
A major challenge in high-precision light-pulse atom interferometric experiments such as in tests of the weak equivalence principle is the uncontrollable dependency of the phase on initial velocity and position of the atoms in the presence…
The synchronization properties of two self-sustained quantum oscillators are studied in the Wigner representation. Instead of considering the quantum limit of the quantum van-der-Pol master equation we derive the quantum master equation…
By using the WKB quantization we deduce an analytical formula for the energy splitting in a double--well potential which is the usual Landau formula with additional quantum corrections. Then we analyze the accuracy of our formula for the…
The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale. By using a perturbative approach, we analytically…
We consider operators of the form H+V where H is the one-dimensional harmonic oscillator and V is a zero-order pseudo-differential operator which is quasi-periodic in an appropriate sense (one can take V to be multiplication by a periodic…
We study a Schr\"odinger-like equation for the anharmonic potential $x^{2 \alpha}+\ell(\ell+1) x^{-2}-E$ when the anharmonicity $\alpha$ goes to $+\infty$. When $E$ and $\ell$ vary in bounded domains, we show that the spectral determinant…
We consider the anharmonic oscillator with an arbitrary-degree anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u" + g_1(x) u' + g_2(x) u + g_3(x) u^n + g_4(x) = 0, n real. Its physical applications…