scholarly journals On some non-Gaussian wave packets

2018 ◽  
Vol 24 (1) ◽  
pp. 109-114
Author(s):  
Alexander E. Patkowski
Keyword(s):  
Wave Function ◽  
Recent Work ◽  
Explicit Formula ◽  
Present Author ◽  
Parabolic Cylinder ◽  
Position Space ◽  
Parabolic Cylinder Function ◽  
Particle Position ◽  
Non Gaussian ◽  
Space Wave

Abstract We expand on a previous study by offering a generalized wave function associated with the parabolic cylinder function and a connection with a two-particle position-space wave function. We also provide an explicit formula for a wave function associated with a recent work by the present author and M. Wolf.

UNITARY TRANSFORMATION APPROACH FOR THE PHASE OF THE DAMPED DRIVEN HARMONIC OSCILLATOR

2003 ◽  
Vol 17 (26) ◽  
pp. 1365-1376 ◽  
Author(s):  
JEONG-RYEOL CHOI
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Unitary Transformation ◽  
Operator Method ◽  
Classical Equation ◽  
Transformation Method ◽  
Invariant Operator ◽  
Harmonic Oscillators ◽  
Parabolic Cylinder ◽  
Parabolic Cylinder Function

Using the invariant operator method and the unitary transformation method together, we obtained discrete and continuous solutions of the quantum damped driven harmonic oscillator. The wave function of the underdamped harmonic oscillator is expressed in terms of the Hermite polynomial while that of the overdamped harmonic oscillator is expressed in terms of the parabolic cylinder function. The eigenvalues of the underdamped harmonic oscillator are discrete while that of the critically damped and the overdamped harmonic oscillators are continuous. We derived the exact phases of the wave function for the underdamped, critically damped and overdamped driven harmonic oscillator. They are described in terms of the particular solutions of the classical equation of motion.

scholarly journals Wave-function engineering via conditional quantum teleportation with a non-Gaussian entanglement resource

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
Warit Asavanant ◽  
Kan Takase ◽  
Kosuke Fukui ◽  
Mamoru Endo ◽  
Jun-ichi Yoshikawa ◽  
...  
Keyword(s):  
Wave Function ◽  
Quantum Teleportation ◽  
Non Gaussian

WEAK CONVERGENCE OF NONLINEAR TRANSFORMATIONS OF INTEGRATED PROCESSES: THE MULTIVARIATE CASE

2009 ◽  
Vol 25 (5) ◽  
pp. 1180-1207 ◽  
Author(s):  
Norbert Christopeit
Keyword(s):  
Weak Convergence ◽  
Recent Work ◽  
Invariance Principle ◽  
Nonlinear Transformations ◽  
New Class ◽  
Triangular Arrays ◽  
Integrable Functions ◽  
Gaussian Case ◽  
Non Gaussian ◽  
Integrated Processes

We consider weak convergence of sample averages of nonlinearly transformed stochastic triangular arrays satisfying a functional invariance principle. A fundamental paradigm for such processes is constituted by integrated processes. The results obtained are extensions of recent work in the literature to the multivariate and non-Gaussian case. As admissible nonlinear transformation, a new class of functionals (so-called locally p-integrable functions) is introduced that adapts the concept of locally integrable functions in Pötscher (2004, Econometric Theory 20, 1–22) to the multidimensional setting.

scholarly journals Computing motivic zeta functions on log smooth models

2019 ◽  
Vol 295 (1-2) ◽  
pp. 427-462 ◽  
Author(s):  
Emmanuel Bultot ◽  
Johannes Nicaise
Keyword(s):  
Zeta Function ◽  
Recent Work ◽  
Explicit Formula ◽  
Essential Role ◽  
Zeta Functions ◽  
Smooth Model ◽  
Motivic Zeta Functions ◽  
Motivic Zeta Function ◽  
Special Case

Abstract We give an explicit formula for the motivic zeta function in terms of a log smooth model. It generalizes the classical formulas for snc-models, but it gives rise to much fewer candidate poles, in general. This formula plays an essential role in recent work on motivic zeta functions of degenerating Calabi–Yau varieties by the second-named author and his collaborators. As a further illustration, we explain how the formula for Newton non-degenerate polynomials can be viewed as a special case of our results.

Recent Work on the Phacopidae

1927 ◽  
Vol 64 (7) ◽  
pp. 308-322 ◽  
Author(s):  
F. R. Cowper Reed
Keyword(s):  
Recent Work ◽  
Present Author ◽  
New Genera ◽  
The World ◽  
Different Parts ◽  
Made In

Since the publication of the paper by the present author in 1905 on the Classification of the Phacopidae, a considerable advance has been made in our knowledge of this family as a result of further and better material being obtained, and of new discoveries in different parts of the world. Many new genera and subgenera have been instituted, and modifications or limitations of some of the old terms have been introduced by various authors. The work of Wedekind, Clarke, Rud. and E. Richter, and Kozlowski has specially dealt with questions of classification, but there is still a considerable amount of diversity in the usage and application of the generic and subgeneric names.

Derivation of Green-type, transitional and uniform asymptotic expansions from differential equations III. The confluent hypergeometric function U ( a , c , z ) for large | c |

1965 ◽  
Vol 284 (1399) ◽  
pp. 531-539 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Confluent Hypergeometric Function ◽  
Parabolic Cylinder ◽  
Exponential Integral ◽  
Parabolic Cylinder Function ◽  
Uniform Expansions ◽  
Kummer's Equation ◽  
Uniform Expansion ◽  
Special Case ◽  
Uniform Asymptotic Expansions

The methods introduced by Jorna (1964 a , b ) are applied to Kummer’s equation, and Green-type, transitional and uniform expansions derived for solutions of the type denoted in Slater (1960) by U ( a , c , z ) which are valid for large | c |. The subsidiary function in the uniform expansion is essentially a parabolic cylinder function of order ½ a . The general exponential integral is studied as a special case. Here the uniform expansion involves as subsidiary function the extensively tabulated error integral.

scholarly journals Precision Measurement of the Position-Space Wave Functions of Gravitationally Bound Ultracold Neutrons

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Y. Kamiya ◽  
G. Ichikawa ◽  
S. Komamiya
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Bound States ◽  
Wave Functions ◽  
Recent Measurement ◽  
Ultracold Neutrons ◽  
Neutron Guide ◽  
Position Space ◽  
Position Sensitive Detectors ◽  
Space Wave

Gravity is the most familiar force at our natural length scale. However, it is still exotic from the view point of particle physics. The first experimental study of quantum effects under gravity was performed using a cold neutron beam in 1975. Following this, an investigation of gravitationally bound quantum states using ultracold neutrons was started in 2002. This quantum bound system is now well understood, and one can use it as a tunable tool to probe gravity. In this paper, we review a recent measurement of position-space wave functions of such gravitationally bound states and discuss issues related to this analysis, such as neutron loss models in a thin neutron guide, the formulation of phase space quantum mechanics, and UCN position sensitive detectors. The quantum modulation of neutron bound states measured in this experiment shows good agreement with the prediction from quantum mechanics.

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