Convergence of the optimized delta expansion for the connected vacuum amplitude: Anharmonic oscillator.
نویسندگان
چکیده
The convergence of the linear δ expansion for the connected generating functional of the quantum anharmonic oscillator is proved. Using an order-dependent scaling for the variational parameter λ, we show that the expansion converges to the exact result with an error proportional to exp(−cN1/3). PACS Numbers : 11.15.Tk, 11.10Jj
منابع مشابه
Convergence of the optimized delta expansion for the connected vacuum amplitude: Zero dimensions.
Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate, N -dependent, choice of an optimizing parameter λ, which is an important feature of the method, the sequence of approximants ZN tends to Z with an error propor...
متن کاملImproved Convergence Proof of the Delta Expansion and Order Dependent Mappings
We improve and generalize in several accounts the recent rigorous proof of convergence of delta expansion order dependent mappings (variational perturbation expansion) for the energy eigenvalues of anharmonic oscillator. For the single-well anharmonic oscillator the uniformity of convergence in g ∈ [0,∞] is proven. The convergence proof is extended also to complex values of g lying on a wide do...
متن کاملOptimized perturbation method for the propagation in the anharmonic oscillator potential
The application of the optimized expansion for the quantum-mechanical propagation in the anharmonic potential λx4 is discussed for real and imaginary time. The first order results in the imaginary time formalism provide approximations to the free energy and particle density which agree well with the exact results in the whole range of temperatures. PACS: 03.65.-w 05.30.-d keywords: quantum mech...
متن کاملOptimized perturbation methods for the free energy of the anharmonic oscillator
Two possibile applications of the optimized expansion for the free energy of the quantum-mechanical anharmonic oscillator are discussed. The first method is for the finite temperature effective potential; the second one, for the classical effective potential. The results of both methods show a quick convergence and agree well with the exact free energy in the whole range of temperatures.
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Physical review. D, Particles and fields
دوره 52 6 شماره
صفحات -
تاریخ انتشار 1995