当前位置: X-MOL 学术Math. Notes › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
New Approach to the Procedure of Quantum Averaging for the Hamiltonian of a Resonance Harmonic Oscillator with Polynomial Perturbation for the Example of the Spectral Problem for the Cylindrical Penning Trap
Mathematical Notes ( IF 0.6 ) Pub Date : 2021-07-06 , DOI: 10.1134/s0001434621050102
E. M. Novikova 1
Affiliation  

Abstract

For the perturbed Hamiltonian of a multifrequency resonance harmonic oscillator, a new approach to calculating the coefficients in the procedure of quantum averaging is proposed. The procedure of quantum averaging is transferred to the space of the graded algebra of symbols by using twisted product introduced in the paper. As a result, the averaged Hamiltonian is represented as a function of generators of the quantum symmetry algebra of the harmonic part of the Hamiltonian. The proposed method is applied to the spectral problem for the Hamiltonian of the cylindrical Penning trap.



中文翻译:

具有多项式微扰的谐振谐波振荡器哈密顿量的量子平均过程的新方法,以圆柱 Penning 陷阱的谱问题为例

摘要

针对多频谐振谐振子的扰动哈密顿量,提出了一种计算量子平均过程中系数的新方法。利用论文中介绍的扭曲乘积,将量子平均的过程转移到符号的梯度代数空间中。结果,平均哈密顿量被表示为哈密顿量调和部分的量子对称代数生成元的函数。将所提出的方法应用于圆柱 Penning 陷阱的哈密顿量的谱问题。

更新日期:2021-07-06
down
wechat
bug