Radial anharmonic oscillator: Perturbation theory, new semiclassical expansion, approximating eigenfunctions. I. Generalities, cubic anharmonicity case
نویسندگان
چکیده
منابع مشابه
Convergent Perturbation Expansion for the Anharmonic Oscillator
We study the ground state as well as the first three excited states of the anharmonic oscillator with anharmonicity hx 4 for a range of h = (0, 10) with the first-order logarithmic perturbation iteration method (FOLPIM). This leads to convergent results. The initial choice of the wave function seems only to affect the rate of convergence in the case of the ground state but may critically affect...
متن کاملA new approach to the logarithmic perturbation theory for the spherical anharmonic oscillator
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the h̄-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both ...
متن کاملConvergence of Scaled Delta Expansion: Anharmonic Oscillator
We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency Ω is chosen to scale with the order as Ω = CN ; 1/3 < γ < 1/2, C > 0 as N → ∞. It converges also for γ = 1/3, if C ≥ αcg, αc ≃ 0.570875, where g is the coupling constant in front of the operator q/4. The extreme case...
متن کامل-Symmetric Cubic Anharmonic Oscillator as a Physical Model
We perform a perturbative calculation of the physical observables, in particular pseudoHermitian position and momentum operators, the equivalent Hermitian Hamiltonian operator, and the classical Hamiltonian for the PT -symmetric cubic anharmonic oscillator, H = 1 2mp 2+ 1 2μ 2x2+iǫx3. Ignoring terms of order ǫ4 and higher, we show that this system describes an ordinary quartic anharmonic oscill...
متن کاملQuartic Anharmonic Oscillator And Random Matrix Theory
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 de nite random hermitean matrices is established. This relationship enables one to present several more or less closed expressions for the oscillator energy. One of such expressions is given in the form of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Modern Physics A
سال: 2019
ISSN: 0217-751X,1793-656X
DOI: 10.1142/s0217751x19501434