Related papers: Precise variational tunneling rates for anharmonic…
In this work, the energy eigenvalues are calculated for the quadratic ($\frac{g^2 x^2}{2}$), pure quartic ($\lambda x^4 $), and quartic anharmonic oscillators ($\frac{g^2 x^2}{2} + \lambda x^4 $) by applying variational method. For this,…
A new variational perturbation theory is developed based on the $q-$deformed oscillator. It is shown that the new variational perturbation method provides 200 or 10 times better accuracy for the ground state energy of anharmonic oscillator…
In a recent work we have proposed an original analytic expression for the partition function of the quartic oscillator. This partition function, which has a simple and compact form with {\it no adjustable parameters}, reproduces some key…
We present a method for extracting tunnelling amplitudes from perturbation expansions which are always divergent and not Borel-summable. We show that they can be evaluated by an analytic continuation of variational perturbation theory. The…
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…
A variationally improved Sturmian approximation for solving time-independent Schr\"odinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian…
A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical anharmonic oscillator and the double-well potential given by $V= m^2 x^2+g x^4$ at arbitrary $g \geq 0$ for…
Using the new variational approach proposed recently for a systematic improvement of the locally harmonic Feynman-Kleinert approximation to path integrals we calculate the partition function of the anharmonic oscillator for all temperatures…
Using the post-Gaussian trial functions, we calculate the variational solutions to the quantum-mechanical anharmonic oscillator. We evaluate not only the ground state but also some excited energies, and compare them with numerical results.
In this work an approximate analytic expression for the quantum partition function of the quartic oscillator described by the potential $V(x) = \frac{1}{2} \omega^2 x^2 + g x^4$ is presented. Using a path integral formalism, the exact…
We present an approximative calculation of the ground-state energy for the anisotropic anharmonic oscillator Using an instanton solution of the isotropic action $\delta = 0$, we obtain the imaginary part of the ground-state energy for small…
Recent advances in the asymptotic analysis of energy levels of potentials produce relative errors in eigenvalue sums of order $10^{-34}$, but few non-trivial potentials have been solved numerically to such accuracy. We solve the general…
In our previous paper I (del Valle--Turbiner, Int. J. Mod. Phys. A34, 1950143, 2019) it was developed the formalism to study the general $D$-dimensional radial anharmonic oscillator with potential $V(r)= \frac{1}{g^2}\,\hat{V}(gr)$. It was…
We will describe how a new, quite simple, but highly effective algorithm, together with the asymptotically fast FFT-based high-precision number multiplication of Mathematica 4 can calculate the ground state of the x^4 anharmonic oscillator…
We present a method for evaluating divergent non-Borel-summable series by an analytic continuation of variational perturbation theory. We demonstrate the power of the method by an application to the exactly known partition function of the…
As an application of a recently developed variational perturbation theory we find the first 22 terms of the convergent strong-coupling series expansion for the ground state energy of the quartic anharmonic oscillator.
The ground state energy of the quartic anharmonic oscillator is calculated by employing the Miller-Good method. For this purpose an extension of the procedure is developed, which is suitable for considering four turning points situations. A…
In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is…
A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Schrodinger equation with a class of phenomenologically useful and methodically challenging anharmonice oscillator potentials V(q)=\alpha_o q^2 +…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…