Rayleighachrodinger perturbation theory with a strong perturbation: anharmonic oscillators
نویسنده
چکیده
The bound state solutions of Schrodinger’s equation for the anharmonic oscillator potentials V = x2+ AxZk ( k = 2 , 3 , . . .) have been investigated, using elementary techniques of low-order variational perturbation theory. For the quartic oscillator ( k = 2) a scaled harmonic potential provides a remarkably accurate model for all A. Although this model is slightly less satisfactory for higher-order anharmonicities ( k 2 3) , our perturbation procedures remain effective, and can be applied successfully provided that higher-order terms are calculated.
منابع مشابه
Convergent Rayleigh–Schrödinger perturbation expansions for low-lying eigenstates and eigenenergies of anharmonic oscillators in intermediate basis states
With suitably chosen unperturbed Hamiltonians, we show numerical evidence of convergence of Rayleigh–Schrödinger perturbation expansions for low-lying eigenstates and the corresponding eigenenergies of the quartic, sextic, and octic anharmonic oscillators, when the anharmonic terms are not very strong. In obtaining the perturbation expansions, unperturbed Hamiltonians are taken as the diagonal ...
متن کاملSome New Analytical Techniques for Duffing Oscillator with Very Strong Nonlinearity
The current paper focuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of the equation of motion; the variational iteration method, He’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. The results reveal that approxim...
متن کاملNumerical results
The strong coupling expansion coefficients for the ordinary and renormalized energies of the ground and first excited states of the quartic, sextic, octic and decadic anharmonic oscillators with the Hamiltonian 2 + 2 + 2 , 2 3 4 5 are computed. The expansion coefficients are also computed for higher excited states of the quartic oscillator. The large-order beha viour of the coefficients, the ra...
متن کاملAn Analytical Technique for Solving Nonlinear Oscillators of the Motion of a Rigid Rod Rocking Bock and Tapered Beams
In this paper, a new analytical approach has been presented for solving strongly nonlinear oscillator problems. Iteration perturbation method leads us to high accurate solution. Two different high nonlinear examples are also presented to show the application and accuracy of the presented method. The results are compared with analytical methods and with the numerical solution using Runge-Kutta m...
متن کاملInverse dimension expansions
Two toy Hamiltonians of anharmonic oscillators are considered. Both of them are found exactly solvable not only in the limit of infinite spatial dimension D but also in the next D ≫ 1 approximation. This makes all their bound states tractable via perturbation series in 1/ √ D ≪ 1.
متن کامل