Journal ArticleDOI
Restrictions on second order response properties of quantum states
TLDR
In this paper, the authors distinguish two extreme classes of perturbation problems depending on the signs of second-order response properties of quantum states, i.e., positive values of the same for any state, and overwhelmingly more probable for highly excited states.Abstract:
We distinguish two extreme classes of perturbation problems depending on the signs of second-order response properties. The first class refers to a positive value of the same for any state, and is overwhelmingly more probable. The other category offers all-but-one negative values, or at least some negative values for highly excited states. The classes are seen to differ in reproducing results of finite-dimensional matrix Hamiltonian perturbations, allowing the emergence of a type of sum rule. A few analytical findings are employed for direct demonstration. The outcomes provide notable restrictions on second order response properties of quantum states.read more
References
More filters
Book ChapterDOI
Recent Developments in Perturbation Theory
TL;DR: Perturbation theory is designed to deal systematically with the effects of small perturbations on physical systems when the effects are mathematically too difficult to calculate exactly, and the properties of the unperturbed system are known as mentioned in this paper.
Journal ArticleDOI
Theory and applications of atomic and ionic polarizabilities
TL;DR: In this paper, a review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.
Journal ArticleDOI
Perturbation theory without wavefunctions
TL;DR: In this article, hypervirial relations are used to yield the series for the energy and other expectation values, for a hydrogen atom with perturbation λ r, without calculation of perturbed wavefunctions.
Journal ArticleDOI
Hypervirial and hellmann--feynman theorems applied to anharmonic oscillators.
TL;DR: In this article, a set of hypervirial theorems plus the Hellman-Feynman theorem are applied to a general anharmonic oscillator and the exact energy and expection values of powers of the position coordinate are expanded in a power series of the coupling constant.