5,566 research outputs found
The Importance of Boundary Conditions in Quantum Mechanics
We discuss the role of boundary conditions in determining the physical
content of the solutions of the Schrodinger equation. We study the
standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary
conditions. As well, we rephrase Feynman's prescription as a
time-asymmetric, causal boundary condition, and discuss the connection of
Feynman's prescription with the arrow of time of Quantum
Electrodynamics. A parallel of this arrow of time with that of Classical
Electrodynamics is made. We conclude that in general, the time evolution of a
closed quantum system has indeed an arrow of time built into the propagators.Comment: Contribution to the proceedings of the ICTP conference "Irreversible
Quantum Dynamics," Trieste, Italy, July 200
A Pedestrian Introduction to Gamow Vectors
The Gamow vector description of resonances is compared with the S-matrix and
the Green function descriptions using the example of the square barrier
potential. By imposing different boundary conditions on the time independent
Schrodinger equation, we obtain either eigenvectors corresponding to real
eigenvalues and the physical spectrum or eigenvectors corresponding to complex
eigenvalues (Gamow vectors) and the resonance spectrum. We show that the poles
of the S matrix are the same as the poles of the Green function and are the
complex eigenvalues of the Schrodinger equation subject to a purely outgoing
boundary condition. The intrinsic time asymmetry of the purely outgoing
boundary condition is discussed. Finally, we show that the probability of
detecting the decay within a shell around the origin of the decaying state
follows an exponential law if the Gamow vector (resonance) contribution to this
probability is the only contribution that is taken into account.Comment: 25 RevTex pages, 3 figure
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets
The analytic continuation of the Lippmann-Schwinger bras and kets is obtained
and characterized. It is shown that the natural mathematical setting for the
analytic continuation of the solutions of the Lippmann-Schwinger equation is
the rigged Hilbert space rather than just the Hilbert space. It is also argued
that this analytic continuation entails the imposition of a time asymmetric
boundary condition upon the group time evolution, resulting into a semigroup
time evolution. Physically, the semigroup time evolution is simply a (retarded
or advanced) propagator.Comment: 32 pages, 3 figure
The role of the rigged Hilbert space in Quantum Mechanics
There is compelling evidence that, when continuous spectrum is present, the
natural mathematical setting for Quantum Mechanics is the rigged Hilbert space
rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is
fully implemented by the rigged Hilbert space rather than just by the Hilbert
space. In this paper, we provide a pedestrian introduction to the role the
rigged Hilbert space plays in Quantum Mechanics, by way of a simple, exactly
solvable example. The procedure will be constructive and based on a recent
publication. We also provide a thorough discussion on the physical significance
of the rigged Hilbert space.Comment: 29 pages, 2 figures; a pedestrian introduction to the rigged Hilbert
spac
College Student Sleep and Quality of Life
Lack of sleep has been found to negatively impact one’s health. Not only can a lack of sleep make one feel tired or impact their mood, there are many other significant health problems that result from less sleep. On the other hand, getting adequate sleep offers several health benefits which may positively influence one’s quality of life. PURPOSE: The aim of the study was to examine the relationship between sleep and quality of life in college students over the age of 18 years old. METHODS: College students of all genders and ethnicities from 18 years of age and older were able to participate in a study assessing the relationship between hours of sleep and quality of life (QOL). Following IRB approval, data was gathered electronically in the Fall of 2021 from college students (eligibility was 18 years+ and enrolled in college) using Qualtrics. The CDC-HRQOL survey was administered along with researcher developed questions on sleep habits. All data was analyzed using a non-parametric Spearman Rank Order Correlation in IBMs SPSS and a 95% confidence interval with a P value RESULTS: No significant correlation between hours of sleep and QOL was found although the relationship was trending (P = 0.069). Therefore, the hypothesis was rejected. CONCLUSION: The findings from this study revealed a trending non-significant correlation between college student hours of sleep and QOL. Further research given the current times and looming COVID-19 pandemic is needed on college students\u27 perceived QOL and sleep. Additionally, assessing sleep habits based on demographics, institution, or status in school (first year, second year, etc.) may help further elucidate the relationship between the variables
On the inconsistency of the Bohm-Gadella theory with quantum mechanics
The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum
Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom
asserts that the solutions of the Lippmann-Schwinger equation are functionals
over spaces of Hardy functions. The preparation-registration arrow of time
provides the physical justification for the Hardy axiom. In this paper, it is
shown that the Hardy axiom is incorrect, because the solutions of the
Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also
shown that the derivation of the preparation-registration arrow of time is
flawed. Thus, Hardy functions neither appear when we solve the
Lippmann-Schwinger equation nor they should appear. It is also shown that the
Bohm-Gadella theory does not rest on the same physical principles as quantum
mechanics, and that it does not solve any problem that quantum mechanics cannot
solve. The Bohm-Gadella theory must therefore be abandoned.Comment: 16 page
Facial identity and emotional expression as predictors during economic decisions
Two sources of information most relevant to guide social decision making are the cooperative tendencies associated with different people and their facial emotional displays. This electrophysiological experiment aimed to study how the use of personal identity and emotional expressions as cues impacts different stages of face processing and their potential isolated or interactive processing. Participants played a modified trust game with 8 different alleged partners, and in separate blocks either the identity or the emotions carried information regarding potential trial outcomes (win or loss). Behaviorally, participants were faster to make decisions based on identity compared to emotional expressions. Also, ignored (nonpredictive) emotions interfered with decisions based on identity in trials where these sources of information conflicted. Electrophysiological results showed that expectations based on emotions modulated processing earlier in time than those based on identity. Whereas emotion modulated the central N1 and VPP potentials, identity judgments heightened the amplitude of the N2 and P3b. In addition, the conflict that ignored emotions generated was reflected on the N170 and P3b potentials. Overall, our results indicate that using identity or emotional cues to predict cooperation tendencies recruits dissociable neural circuits from an early point in time, and that both sources of information generate early and late interactive patterns
Genomic resources in chickpea
Chickpea has considerably increased the genomic resources in recent years providing highly saturated genetic maps including anonymous or gene-specific markers targeting some agronomic traits of interest. In addition, the publication of the two draft genome sequences of Kabuli and Desi chickpea types opens a new era in genomic tools. Furthering in our understanding of the association between phenotypic traits (Quantitative Trait loci-QTL-or genes) with the transcriptome and gene annotation provided by genome sequencing data will be the future challenge to be able to exploit with success marker-assisted Selection(MAS)
- …