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An Introductory History of Quantum Mechanics-II
Published in Shabnam Siddiqui, Quantum Mechanics, 2018
Wave Packet: A particle is well localized in space, and a wave spreads through space. Thus, associating a wave with a particle implies that the wave is localized because particle must be located somewhere in space. It is conceptually quite contradictory to associate a wave with a particle. This logical difficulty can only be removed by assuming that the wave associated with a particle can only be represented as a wave packet. A wave packet is comprised of a group of waves of slightly different wavelengths, with corresponding phases and amplitudes that interfere constructively over only a small region of space. Outside of that region, they produce an amplitude that rapidly diminishes to zero as a result of destructive interference. Figure 2.3 depicts such a wave packet.
Fundamentals of Quantum Nanoelectronics
Published in Razali Ismail, Mohammad Taghi Ahmadi, Sohail Anwar, Advanced Nanoelectronics, 2018
Jeffrey Frank Webb, Mohammad Taghi Ahmadi
Some insight into the uncertainty principle and how it is related to waves can be appreciated by considering wave packets. To start with, assume a quantum object localized over a small region of space. It can be represented by a superposition of plane waves a(k)e−i[ω(k)t−k·r] of the form () Ψ(x,t)=∫over k-spacea(k)e−i[ω(k)t−k⋅r]dVk.
Duality of Light and Matter
Published in Zbigniew Ficek, Quantum Physics for Beginners, 2017
In the next step of our efforts to understand the fundamentals of quantum physics, we will explain why in quantum physics a localized particle is represented by a superposition of wave functions (wave packet) rather than a single harmonic wave function. Important steps on the way to understand the concept of wave packets are the uncertainty principle between the position and momentum of the particle, and the superposition principle.
On the group velocity of Love-type waves in composite structure loaded with viscous fluid
Published in Waves in Random and Complex Media, 2022
Kamlesh Kumar Pankaj, Sanjeev Anand Sahu, Shreeta Kumari
A properly designed Love-type wave sensor is very promising for bio-sensing because of its high sensitivity. Love-type wave has a pure shear horizontal polarization and therefore no elastic interaction with an ideal liquid. This property makes it particularly interesting for bio-sensing in a liquid environment. Kovacs et al. [18] gave the experimental result of the Love-type wave propagation in biochemical sensing in liquids. Propagation of wave in liquid loaded composite structure is studied by Du et al. [19]. Wu and Wu [20] have used the sextic formalism for the solution of Rayleigh and Love wave propagation in a composite loaded with viscous fluid. The development of acoustic wave sensor in bio-sensing created the need for further investigation of the surface wave propagation in a viscous liquid loaded layered medium. A wave packet or wave group consists of a superposition of several waves with different frequencies. When harmonic waves with different frequencies interfere in a dispersive medium, the modulation wave propagates at group velocity. Generally, the group velocity corresponds to the propagation of energy. Thus, the investigation of group velocity and its properties become valuable.
Classifier for the functional state of the respiratory system via descriptors determined by using multimodal technology
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2023
Sergey Alekseevich Filist, Riad Taha Al-kasasbeh, Olga Vladimirovna Shatalova, Altyn Amanzholovna Aikeyeva, Osama M. Al-Habahbeh, Mahdi Salman Alshamasin, Korenevskiy Nikolay Alekseevich, Mohammad Khrisat, Maksim Borisovich Myasnyankin, Maksim Ilyash
The ECS spectrum (Figure 3) consists of spectral trains, the centers of which are multiples of the fundamental ECS harmonic of approximately 1 Hz. In this case, we are only interested in the RR spectrum, which is deployed in the region of the first train and whose diagram is shown on the right in Figure 3. However, it is very difficult to distinguish the variability of the respiratory rhythm from such a spectrum (Hanna et al. 2020). Therefore, to study slow waves in a respiratory train, we will use time-frequency transformations, where the most common of which is the wavelet transform (Jeon et al. 2019). In physics, a wave packet (WP) or wave train is a short ‘burst’ or ‘envelope’ of localized wave action that travels as a unit.