Self-adjoint extensions of the Hamiltonian operator with symmetric potentials which are unbounded from below

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Title:	Self-adjoint extensions of the Hamiltonian operator with symmetric potentials which are unbounded from below
Authors:	Cho, Hing-tong;Ho, Choon-lin
Contributors:	淡江大學物理學系
Date:	2008-06
Issue Date:	2013-03-12 10:58:00 (UTC+8)
Publisher:	Bristol: Institute of Physics Publishing Ltd.
Abstract:	We study the self-adjoint extensions of the Hamiltonian operator with symmetric potentials which go to −∞ faster than −\|x\|2p with p > 1 as x → ±∞. In this extension procedure, one requires the Wronskian between any states in the spectrum to approach to the same limit as x → ±∞. Then the boundary terms cancel and the Hamiltonian operator can be shown to be Hermitian. Discrete bound states with even and odd parities are obtained. Since the Wronskian is not required to vanish asymptotically, the energy eigenstates could be degenerate. Some explicit examples are given and analyzed.
Relation:	Journal of Physics A: Mathematical and theoretical 41(25), 255308(11pages)
DOI:	10.1088/1751-8113/41/25/255308
Appears in Collections:	[Graduate Institute & Department of Physics] Journal Article

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