skip to main content

SciTech ConnectSciTech Connect

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

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.
Authors:
;  [1]
  1. ─░stanbul Technical University, Informatics Institute, Maslak, 34469, ─░stanbul (Turkey)
Publication Date:
OSTI Identifier:
22499187
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1702; Journal Issue: 1; Conference: ICCMSE 2015: International conference of computational methods in sciences and engineering 2015, Athens (Greece), 20-23 Mar 2015; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DEGREES OF FREEDOM; EIGENFUNCTIONS; EIGENSTATES; EIGENVALUES; EXPECTATION VALUE; HAMILTONIANS; HYDROGEN; POSITION OPERATORS; QUANTUM SYSTEMS; WAVE FUNCTIONS