Positive width function and energy indeterminacies in ammonia molecule

Douvropoulos, TG

dc.contributor.author	Douvropoulos, TG	en
dc.date.accessioned	2014-03-01T02:44:55Z
dc.date.available	2014-03-01T02:44:55Z
dc.date.issued	2007	en
dc.identifier.issn	0020-7608	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/32018
dc.subject	Action	en
dc.subject	Ammonia	en
dc.subject	Complex poles	en
dc.subject	Double well	en
dc.subject	Energy variations	en
dc.subject	Inversion frequency	en
dc.subject	Positive width function	en
dc.subject	Tunneling	en
dc.subject	Tunneling time	en
dc.subject	Turning points	en
dc.subject.classification	Chemistry, Physical	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Physics, Atomic, Molecular & Chemical	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Electron tunneling	en
dc.subject.other	Energy conservation	en
dc.subject.other	Energy gap	en
dc.subject.other	Green's function	en
dc.subject.other	Nitrogen	en
dc.subject.other	Semiconductor quantum wells	en
dc.subject.other	Complex poles	en
dc.subject.other	Double well	en
dc.subject.other	Energy indeterminacies	en
dc.subject.other	Energy spectrum	en
dc.subject.other	Inversion frequency	en
dc.subject.other	Path integral theory	en
dc.subject.other	Positive width function	en
dc.subject.other	Tunneling time	en
dc.subject.other	Ammonia	en
dc.title	Positive width function and energy indeterminacies in ammonia molecule	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1002/qua.21243	en
heal.identifier.secondary	http://dx.doi.org/10.1002/qua.21243	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	A recently published methodology based on the semiclassical path integral theory was applied in a double well structure and gave the analytic form of the system's Green's function. This type of potential can describe the ammonia molecule as far as the motion of the nitrogen atom perpendicular to the hydrogen plane is discussed. Because of the fact that a double well describes a bound system and correspondingly stationary states (constructed by the symmetric and antisymmetric superposition of the eigenstates of the two unperturbed wells), it was expected that the energy spectrum would be real, in a form of doublets due to the splitting effect that takes place. However, the result was a pair of complex poles, which had a clearly positive imaginary part for each member. The present work explains the role of the imaginary parts of the complex poles as the decay rate of quantities defined as the energy indeterminacies, which are directly related to the fact that energy is not well determined in a classically forbidden region of motion. These quantities come as a function of (d kappa)/dE, which is the derivative of the classical action inside the potential barrier, with respect to energy. The major contribution comes from the turning points, and then the imaginary parts are responsible, not only for the conservation of energy, but for the correct sign of time as well. In this way, a different approach for the tunneling process is adopted, in which the entry or exit of the particle from the potential barrier takes place inside a neighborhood of the turning point, as though the latter was broadened and fluctuating. The magnitude of the previously mentioned decay rate is equal to omega/pi, where omega is the frequency of the classical oscillations inside one well. In contrast, the inversion frequency is generated by the part of the complex pole that is unrelated to (d kappa)/dE and is much smaller in magnitude than the classical frequency, since it is given as omega/pi exp(-kappa). In this way, the period of the energy fluctuations is much smaller than the internal period of the system produced by the oscillating communication of the two classically allowed regions of motion. (c) 2006 Wiley Periodicals, Inc.	en
heal.publisher	WILEY-BLACKWELL	en
heal.journalName	International Journal of Quantum Chemistry	en
dc.identifier.doi	10.1002/qua.21243	en
dc.identifier.isi	ISI:000245839300003	en
dc.identifier.volume	107	en
dc.identifier.issue	8	en
dc.identifier.spage	1673	en
dc.identifier.epage	1687	en