Posted by 
By Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov (auth.)
This ebook introduces systematically the operator procedure for the answer of the Schrödinger equation. this technique allows to explain the states of quantum platforms within the whole diversity of parameters of Hamiltonian with a predefined accuracy. The operator technique is exclusive in comparison with different non-perturbative equipment because of its skill to carry in zeroth approximation the uniformly appropriate estimate for either flooring and excited states of quantum approach. the strategy has been generalized for the applying to quantum information and quantum box conception. during this publication, the varied functions of operator technique for varied actual structures are verified. uncomplicated types are used to demonstrate the fundamental ideas of the strategy that are additional used for the answer of complicated difficulties of quantum idea for many-particle structures. the consequences received are supplemented by means of numerical calculations, offered as tables and figures.
Read Online or Download Non-perturbative Description of Quantum Systems PDF
Best quantum theory books
Professor E. U. Condon's the idea of Atomic Spectra used to be the 1st entire publication at the electron constitution of atoms, and has turn into a world-renowned vintage. initially released in 1980, Atomic constitution was once the overdue Professor Condon's ultimate contribution to the literature of this box. accomplished via his colleague and previous pupil Halis Odabşi, this booklet used to be one of many first built-in bills of the topic to incorporate such advancements as crew concept techniques and Racah tools.
This is often the 3rd, considerably accelerated variation of the great textbook released in 1990 at the conception and functions of course integrals. it's the first booklet to explicitly resolve course integrals of a wide selection of nontrivial quantum-mechanical structures, specifically the hydrogen atom. The recommendations became attainable by means of significant advances.
Quantum Field Theory I: Foundations and Abelian and Non-Abelian Gauge Theories
This textbook covers a large spectrum of advancements in QFT, emphasizing these features which are now good consolidated and for which passable theoretical descriptions were supplied. The publication is exclusive in that it deals a brand new method of the topic and explores many subject matters basically touched upon, if lined in any respect, in usual reference works.
Additional resources for Non-perturbative Description of Quantum Systems
Sample text
55) where ! 0 '1 D I 2.! C ! 0 / p 2 !! 0 '2 D ln : ! pn 2! n R.! /jn C ki C 1jR.! /jn C ki : n C 1hn C 1jR.! s x03 8/ 8/ n2 ! 0/ Here we have taken into account the normalizing condition hnj n i D 1 for the wave functions. 6. 49). This operation is required for the description of real physical systems, when the potential parameters have to be found for given frequencies of transitions between energy levels (inverse problem of spectroscopy [53]). 49). C 1 4 1 ! 1 4! a2 4! 2nO C 1/I HO 1 D 1 4 Á 2 !
5. 3 Calculation Accuracy of the Wave Function The results of the previous sections demonstrate the ability of OM to find the QAO eigenvalue spectrum with any required accuracy. However, for any method dedicated to the solution of SE, the precision of the eigenfunction calculation is even more important test because of the useability of eigenfunctions for various applications. 49) for further approximations. The case appears to be simple when we calculate the diagonal matrix elements since they are reduced to the well-known matrix elements of the transition between the harmonic oscillator states.
The similar condition is used for the solution of the Eq. 13). 30) in the Eq. 32) k¤n We omit the index ! HO 1 /nk Á Hnk ; k ¤ n: The equations for the coefficients Cnm are found by projecting the Eq. 34) the expressions for the diagonal matrix elements Hnn and non-zero transition matrix elements Hnk in the case of QAO can be found: Á 1 3 2 1 C 2n C 2n I .! 1 C 2n/ C 4! 4! n C 2/ 1 !! 2n C 3/ I Hnn D Hn;nC2 Hn;nC4 D HnC4;n D q 4! 29). As mentioned above, the dependence of the coefficients Cnk on the parameter !