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On the Interaction of an Isolated State with the Known Infinite-dimensional Quantum System

Tomislav P. Živković ; Ruđer Bošković Institute, P. O. Box 180, HR-10002 Zagreb, Croatia

Sažetak

The interaction of an isolated state |Θ〉 with a known infinite-dimensional quantum system S_∞ b containing multiple eigenvalue bands is considered. An example is the interaction of an isolated molecular state with the electromagnetic field. This problem is the main subject of spectroscopy. Another example is the interaction of an isolated molecular state of a molecule situated on the surface of a solid with this solid. This is the subject of the surface state physics. Such problems are usually treated within the formalism of the perturbation expansion. Recently a new mathematical method for the treatment of such problems was suggested. This method produces correct solution of the combined system, however strong the interaction between the state |Θ〉 and the system S_∞ b . Key quantities in this method are characteristic functions f_v(ε) and functions ω_v(ε). Functions f_v(ε) are constructed from the quantities describing unperturbed system S_∞ b and from the known interaction of this system with the state |Θ〉. Functions ω_v(ε) are then expressed in terms of the characteristic functions f_v(ε). An important mathematical problem is the calculation of the functions ω_v(ε), once functions f_v(ε) are known. A general mathematical solution to this problem is obtained for the case when characteristic functions f_v(ε) are polynomials. Since each function which is continuous in a finite interval can be approximated (to any desired degree of accuracy) with some polynomial, this solution presents an important mathematical tool for the practical application of the suggested method. Obtained results are illustrated with few model examples of the interaction of an isolated state with an infinite quantum system.

Ključne riječi

interaction of quantum systems; perturbation; eigenvalues; eigenstates

Hrčak ID:

102676

URI

https://hrcak.srce.hr/102676

Datum izdavanja:

31.5.2004.

Posjeta: 938 *