dorsal/arxiv
View SchemaQuantum mechanics in general quantum systems (II): Perturbation theory
| Authors | An Min Wang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611217 |
| URL | https://arxiv.org/abs/quant-ph/0611217 |
Abstract
We propose an improved scheme of perturbation theory based on our exact solution [An Min Wang, quant-ph/0611216] in general quantum systems independent of time. Our elementary start-point is to introduce the perturbing parameter as late as possible. Our main skills are Hamiltonian redivision so as to overcome a flaw of the usual perturbation theory, and the perturbing Hamiltonian matrix product decomposition in order to separate the contraction and anti-contraction terms. Our calculational technology is the limit process for eliminating apparent divergences. Our central idea is ``dynamical rearrangement and summation" for the sake of the partial contributions from the high order even all order approximations absorbed in our perturbed solution. Consequently, we obtain the improved forms of the zeroth, first, second and third order perturbed solutions absorbing the partial contributions from the high order even all order approximations of perturbation. Then we deduce the improved transition probability. In special, we propose the revised Fermi's golden rule. Moreover, we apply our scheme to obtain the improved forms of perturbed energy and perturbed state. In addition, we study an easy understanding example of two-state system to illustrate our scheme and show its advantages. All of this implies the physical reasons and evidences why our improved scheme of perturbation theory are actually calculable, operationally efficient, conclusively more accurate. Our improved scheme is the further development and interesting application of our exact solution, and it has been successfully used to study on open system dynamics [An Min Wang, quant-ph/0601051].
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"abstract": "We propose an improved scheme of perturbation theory based on our exact\nsolution [An Min Wang, quant-ph/0611216] in general quantum systems independent\nof time. Our elementary start-point is to introduce the perturbing parameter as\nlate as possible. Our main skills are Hamiltonian redivision so as to overcome\na flaw of the usual perturbation theory, and the perturbing Hamiltonian matrix\nproduct decomposition in order to separate the contraction and anti-contraction\nterms. Our calculational technology is the limit process for eliminating\napparent divergences. Our central idea is ``dynamical rearrangement and\nsummation\" for the sake of the partial contributions from the high order even\nall order approximations absorbed in our perturbed solution. Consequently, we\nobtain the improved forms of the zeroth, first, second and third order\nperturbed solutions absorbing the partial contributions from the high order\neven all order approximations of perturbation. Then we deduce the improved\ntransition probability. In special, we propose the revised Fermi\u0027s golden rule.\nMoreover, we apply our scheme to obtain the improved forms of perturbed energy\nand perturbed state. In addition, we study an easy understanding example of\ntwo-state system to illustrate our scheme and show its advantages. All of this\nimplies the physical reasons and evidences why our improved scheme of\nperturbation theory are actually calculable, operationally efficient,\nconclusively more accurate. Our improved scheme is the further development and\ninteresting application of our exact solution, and it has been successfully\nused to study on open system dynamics [An Min Wang, quant-ph/0601051].",
"arxiv_id": "quant-ph/0611217",
"authors": [
"An Min Wang"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"physics.atom-ph"
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"title": "Quantum mechanics in general quantum systems (II): Perturbation theory",
"url": "https://arxiv.org/abs/quant-ph/0611217"
},
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