Εξειδίκευση τύπου :	Άρθρο σε επιστημονικό περιοδικό
Τίτλος:	Correct small-truncated excited state wave functions obtained via minimization principle for excited states compared/ opposed to Hylleraas-Undheim and McDonald higher ''roots''
Δημιουργός/Συγγραφέας:	Xiong Z. Zang J. Liu H.J. Karaoulanis D. Zhou Q. [EL] Μπακάλης, Ναούμ Χ.[EN] Bacalis, Naoum C.
Εκδότης:	IOS Press
Ημερομηνία:	2017
Γλώσσα:	Αγγλικά
ISSN:	1472-7978
DOI:	10.3233/JCM-170722
Περίληψη:	We demonstrate that, if a truncated expansion of a wave function is large, then the standard excited states computational method, of optimizing one ''root'' of a secular equation, according to the theorem of Hylleraas, Undheim and McDonald (HUM), tends to the correct excited wave function, comparable to that obtained via our proposed minimization principle for excited states [J. Comput. Meth. Sci. Eng. 8, 277 (2008)] (independent of orthogonality to lower lying approximants). However, if a truncated expansion of a wave function is small - that would be desirable for large systems - then the HUM-based methods may lead to an incorrect wave function - despite the correct energy (: According to the HUM theorem) whereas our method leads to correct, reliable, albeit small truncated wave functions. The demonstration is done in He excited states, using truncated series ''small'' expansions both in Hylleraas coordinates, and via standard configuration-interaction truncated ''small'' expansions, in comparison with corresponding ''large'' expansions. Beyond that, we give some examples of linear combinations of Hamiltonian eigenfunctions that have the energy of the 1 st excited state, albeit they are orthogonal to it, demonstrating that the correct energy is not a criterion of correctness of the wave function.
Τίτλος πηγής δημοσίευσης:	Journal of Computational Methods in Sciences and Engineering
Τόμος/Κεφάλαιο:	17
Τεύχος:	3
Σελίδες:	347-361
Θεματική Κατηγορία:	[EL] Φυσική και θεωρητική χημεία[EN] Physical and theoretical chemistry [EL] Ατομική φυσική (συμπ. μοριακή φυσική, σχετικότητα, κβαντική θεωρία και φυσική στερεάς κατάστασης)[EN] Atomic physics (Incl. molecular physics, relativity, quantum theory, and solid state physics)
Λέξεις-Κλειδιά:	Excited states HUM minimization principle
Αξιολόγηση από ομότιμους (peer reviewed):	Ναι
Κάτοχος πνευματικών δικαιωμάτων:	© 2017 IOS Press and the authors.
Όροι και προϋποθέσεις δικαιωμάτων:	All Open Access, Green
Εμφανίζεται στις συλλογές:	Ινστιτούτο Θεωρητικής και Φυσικής Χημείας (ΙΘΦΧ) - Επιστημονικό έργο