scholarly journals Wave Packets of Mandelbrot Type in Boundary Problems of Quantum Mechanics

2018 ◽  
Vol 09 (02) ◽  
Author(s):  
Igor B Krasnyuk
Keyword(s):  
Quantum Mechanics ◽  
Wave Packets ◽  
Boundary Problems

scholarly journals Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 96 ◽  
Author(s):  
Georgi Gary Rozenman ◽  
Shenhe Fu ◽  
Ady Arie ◽  
Lev Shemer
Keyword(s):  
Quantum Mechanics ◽  
Gravity Waves ◽  
Water Waves ◽  
Water Wave ◽  
Wave Packets ◽  
Theoretical Models ◽  
Surface Gravity ◽  
Finite Width ◽  
Self Healing ◽  
Surface Gravity Waves

We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

TOPOLOGICAL EFFECTS IN QUANTUM MECHANICS AND HIGH VELOCITY ESTIMATES

2011 ◽  
Vol 20 (05) ◽  
pp. 951-961 ◽  
Author(s):  
RICARDO WEDER
Keyword(s):  
Exact Solution ◽  
Quantum Mechanics ◽  
Error Bounds ◽  
High Velocity ◽  
Wave Packets ◽  
Finite Energy ◽  
Time Dependent ◽  
Rigorous Proof ◽  
Bohm Effect ◽  
Aharonov Bohm

We consider the problem of obtaining high-velocity estimates for finite energy solutions (wave packets) to Schrödinger equations for N-body systems. We discuss a time-dependent method that allows us to obtain precise estimates with error bounds that decay as a power of the velocity. We apply this method to the electric Aharonov–Bohm effect. We give the first rigorous proof that quantum mechanics predicts the existence of this effect. Our result follows from an estimate in norm, uniform in time, that proves that the Aharonov–Bohm Ansatz is a good approximation to the exact solution to the Schrödinger equation for high velocity.

Memories of electrons in crystals

1980 ◽  
Vol 371 (1744) ◽  
pp. 24-27 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Wave Packets ◽  
Radiation Damping ◽  
Theoretical Physics ◽  
Wave Mechanics ◽  
Good Fortune ◽  
First Time

As a student in Zurich, it was my good fortune to be present at the colloquium in which Schrödinger told the first time about his wave mechanics. When both he and Debye accepted positions in Germany I decided upon the latter’s advice to continue my studies under Heisenberg in Leipzig, where I arrived in the autumn of 1927. Already in Zurich my interests had turned from experimental to theoretical physics, and particularly towards quantum mechanics, and before coming to Leipzig I had started some calculations on the radiation-damping of wave-packets. As the first thing, Heisenberg encouraged me to complete this work, later published in the Physikalische Zeitschrift , whereupon he considered me ready to start on a topic for my Ph.D. thesis.

scholarly journals Beyond Superconductivity

2019 ◽  
Vol 33 (1) ◽  
pp. 249-251
Author(s):  
Jochen Mannhart
Keyword(s):  
Quantum Mechanics ◽  
Wave Packets ◽  
Quantum States ◽  
Quantum Mechanical ◽  
Transition Regime ◽  
Unitary Evolution ◽  
Classical Physics ◽  
Schrödinger’S Equation ◽  
Novel Device ◽  
Schrödinger's Equation

Abstract We present a novel device concept that utilizes the fascinating transition regime between quantum mechanics and classical physics. The devices operate by using a small number of individual quantum mechanical collapse events to interrupt the unitary evolution of quantum states represented by wave packets. Exceeding the constraints of the unitary evolution of quantum mechanics given by Schrödinger’s equation and of classical Hamiltonian physics, these devices display a surprising behavior.

Quantum healing of spacetime singularities: A review

2018 ◽  
Vol 33 (04) ◽  
pp. 1830002
Author(s):  
D. A. Konkowski ◽  
T. M. Helliwell
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Spacetime Singularities ◽  
Wave Packets ◽  
Geodesic Paths ◽  
Quantum Wave ◽  
General Relativistic ◽  
Alternative Approaches

Singularities are commonplace in general relativistic spacetimes. It is natural to hope that they might be “healed” (or resolved) by the inclusion of quantum mechanics, either in the theory itself (quantum gravity) or, more modestly, in the description of the spacetime geodesic paths used to define them. We focus here on the latter, mainly using a procedure proposed by Horowitz and Marolf to test whether singularities in broad classes of spacetimes can be resolved by replacing geodesic paths with quantum wave packets. We list the spacetime singularities that various authors have studied in this context, and distinguish those which are healed quantum mechanically (QM) from those which remain singular. Finally, we mention some alternative approaches to healing singularities.

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