An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom

Berfin Kalay; Metin Demiralp

doi:10.1063/1.4938943

An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom

Berfin Kalay, Metin Demiralp

Faculty of Computer and Informatics

Istanbul Technical University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Citations (Scopus)

Abstract

This proceedings paper aims to show the efficiency of an expectation value identity for a given algebraic function operator which is assumed to be depending pn only position operator. We show that this expectation value formula becomes enabled to determine the eigenstates of the quantum system Hamiltonian as long as it is autonomous and an appropriate basis set in position operator is used. This approach produces a denumerable infinite recursion which may be considered as revisited but at the same time generalized form of the recursions over the natural number powers of the position operator. The content of this short paper is devoted not only to the formulation of the new method but also to show that this novel approach is capable of catching the eigenvalues and eigenfunctions for Hydrogen-like systems, beyond that, it can give a hand to us to reveal the wavefunction structure. So it has also somehow a confirmative nature.

Original language	English
Title of host publication	International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015
Editors	Zacharoula Kalogiratou, Theodore E. Simos, Theodore Monovasilis, Theodore E. Simos, Theodore E. Simos
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735413498
DOIs	https://doi.org/10.1063/1.4938943
Publication status	Published - 31 Dec 2015
Event	International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015 - Athens, Greece Duration: 20 Mar 2015 → 23 Mar 2015

Publication series

Name	AIP Conference Proceedings
Volume	1702
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015
Country/Territory	Greece
City	Athens
Period	20/03/15 → 23/03/15

Bibliographical note

Publisher Copyright:
© 2015 AIP Publishing LLC.

Keywords

Algebraic function operators
Expectation values
Hydrogen-like systems
Quantum dynamical evolutions

Access to Document

10.1063/1.4938943

Cite this

Kalay, B., & Demiralp, M. (2015). An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom. In Z. Kalogiratou, T. E. Simos, T. Monovasilis, T. E. Simos, & T. E. Simos (Eds.), International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015 Article 170008 (AIP Conference Proceedings; Vol. 1702). American Institute of Physics Inc.. https://doi.org/10.1063/1.4938943

Kalay, Berfin ; Demiralp, Metin. / An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom. International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015. editor / Zacharoula Kalogiratou ; Theodore E. Simos ; Theodore Monovasilis ; Theodore E. Simos ; Theodore E. Simos. American Institute of Physics Inc., 2015. (AIP Conference Proceedings).

@inproceedings{816be291f009499290aea721e9cfee75,

title = "An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom",

abstract = "This proceedings paper aims to show the efficiency of an expectation value identity for a given algebraic function operator which is assumed to be depending pn only position operator. We show that this expectation value formula becomes enabled to determine the eigenstates of the quantum system Hamiltonian as long as it is autonomous and an appropriate basis set in position operator is used. This approach produces a denumerable infinite recursion which may be considered as revisited but at the same time generalized form of the recursions over the natural number powers of the position operator. The content of this short paper is devoted not only to the formulation of the new method but also to show that this novel approach is capable of catching the eigenvalues and eigenfunctions for Hydrogen-like systems, beyond that, it can give a hand to us to reveal the wavefunction structure. So it has also somehow a confirmative nature.",

keywords = "Algebraic function operators, Expectation values, Hydrogen-like systems, Quantum dynamical evolutions",

author = "Berfin Kalay and Metin Demiralp",

note = "Publisher Copyright: {\textcopyright} 2015 AIP Publishing LLC.; International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015 ; Conference date: 20-03-2015 Through 23-03-2015",

year = "2015",

month = dec,

day = "31",

doi = "10.1063/1.4938943",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Zacharoula Kalogiratou and Simos, {Theodore E.} and Theodore Monovasilis and Simos, {Theodore E.} and Simos, {Theodore E.}",

booktitle = "International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015",

}

Kalay, B & Demiralp, M 2015, An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom. in Z Kalogiratou, TE Simos, T Monovasilis, TE Simos & TE Simos (eds), International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015., 170008, AIP Conference Proceedings, vol. 1702, American Institute of Physics Inc., International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015, Athens, Greece, 20/03/15. https://doi.org/10.1063/1.4938943

An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom. / Kalay, Berfin; Demiralp, Metin.
International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015. ed. / Zacharoula Kalogiratou; Theodore E. Simos; Theodore Monovasilis; Theodore E. Simos; Theodore E. Simos. American Institute of Physics Inc., 2015. 170008 (AIP Conference Proceedings; Vol. 1702).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom

AU - Kalay, Berfin

AU - Demiralp, Metin

PY - 2015/12/31

Y1 - 2015/12/31

N2 - This proceedings paper aims to show the efficiency of an expectation value identity for a given algebraic function operator which is assumed to be depending pn only position operator. We show that this expectation value formula becomes enabled to determine the eigenstates of the quantum system Hamiltonian as long as it is autonomous and an appropriate basis set in position operator is used. This approach produces a denumerable infinite recursion which may be considered as revisited but at the same time generalized form of the recursions over the natural number powers of the position operator. The content of this short paper is devoted not only to the formulation of the new method but also to show that this novel approach is capable of catching the eigenvalues and eigenfunctions for Hydrogen-like systems, beyond that, it can give a hand to us to reveal the wavefunction structure. So it has also somehow a confirmative nature.

AB - This proceedings paper aims to show the efficiency of an expectation value identity for a given algebraic function operator which is assumed to be depending pn only position operator. We show that this expectation value formula becomes enabled to determine the eigenstates of the quantum system Hamiltonian as long as it is autonomous and an appropriate basis set in position operator is used. This approach produces a denumerable infinite recursion which may be considered as revisited but at the same time generalized form of the recursions over the natural number powers of the position operator. The content of this short paper is devoted not only to the formulation of the new method but also to show that this novel approach is capable of catching the eigenvalues and eigenfunctions for Hydrogen-like systems, beyond that, it can give a hand to us to reveal the wavefunction structure. So it has also somehow a confirmative nature.

KW - Algebraic function operators

KW - Expectation values

KW - Hydrogen-like systems

KW - Quantum dynamical evolutions

UR - http://www.scopus.com/inward/record.url?scp=84984566997&partnerID=8YFLogxK

U2 - 10.1063/1.4938943

DO - 10.1063/1.4938943

M3 - Conference contribution

AN - SCOPUS:84984566997

T3 - AIP Conference Proceedings

BT - International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015

A2 - Kalogiratou, Zacharoula

A2 - Simos, Theodore E.

A2 - Monovasilis, Theodore

A2 - Simos, Theodore E.

PB - American Institute of Physics Inc.

T2 - International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015

Y2 - 20 March 2015 through 23 March 2015

ER -

Kalay B, Demiralp M. An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom. In Kalogiratou Z, Simos TE, Monovasilis T, Simos TE, Simos TE, editors, International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015. American Institute of Physics Inc. 2015. 170008. (AIP Conference Proceedings). doi: 10.1063/1.4938943

An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this