Can Quantum Mechanical Two-State Theory model Coulomb’s Force?
The quantum mechanical description of the four fundamental forces of nature is very important for the decryption of the rules which underlie our world. While Quantum Electrodynamics (QED) describes the electromagnetic force in great detail, it also uses complex mathematical techniques and advanced physical concepts. In the following, I will analyze to what extent a quantum mechanical two-state model can be used to describe the Coulomb interaction between two charged particles. To do so, I will exclusively focus on the electrostatic interaction, leaving dynamics aside. Furthermore, the analysis is nonrelativistic and does not consider the spin of the particles. Finally, using discrete state theory allows to explore the strength of the basic concepts of early quantum mechanics. In this sense, I will try to develop a simpli ed model for the quantum mechanical description of the electrostatic force. However, the analysis is not simplistic, since the traditional formalism of quantum mechanics will be used, including Dirac's Bra-ket notation, probability amplitudes, the Hamiltonian matrix as well as the Schrödinger equation. To understand the framework of my project, it may be helpful to take a look at the source of inspiration for my analysis: In Chapter 10 of the third volume of the well-known textbook series The Feynman Lectures on Physics[4], the force holding the hydrogen molecular ion together is explained in terms of a two-state system. The electron of the molecular ion can be either at the rst proton or at the second one. The exchange of the electron between both protons leads to an attractive force between them. It is known from QED that the electrostatic interaction between two charged particles is due to the exchange of a virtual photon which acts as force carrier. The idea of my work is to explore whether the electrostatic force can be described by a very similar model, replacing the electron acting as force carrier in the molecular ion by a virtual photon for the description of the electrostatic force between two charged particles. To describe a system consisting of charged particles, I will make the assumption that a charged particle can appear in two states. Either it is in state e where it can emit a photon or it is in state a which enables it to absorb a photon. Upon emission or absorption of a photon the charged particle transitions to the respective other state. This makes the approach analyzed in my work an element of discrete state theory, since two di erent states of the particle are used to store information about it. Of course such a model cannot be compared to the sophisticated theory of Quantum Electrodynamics. The point is, however, that it is interesting to explore the power of the most fundamental concepts of quantum mechanics and to show that such an analysis can lead to inspiring results.
Efficient Modelling of Aeroacoustic Phenomena in Seebeck Sirens: A Simplified Approach for Real-World Applications
This paper presents a simplified but mostly accurate model for the acoustic mechanism of Seebeck sirens. We investigate the impact of key parameters, including the number and size of holes, as well as the angular speed of the disk, on the characteristics of the produced sound. The disk is fabricated using fused deposition modelling 3D printing, and we used a brushless motor, an air compressor, and a shotgun microphone to capture the generated sound. An order of magnitude analysis was conducted on the Navier-Stokes equation to formulate a simplified version. These simplifications allowed for a low computational intensity model relating volume flow rate to sound pressure level, which is used to predict the waveform of sound produced. Our findings reveal that the fundamental frequency of the sound can be precisely predicted by only the rotational frequency of the disk and the number of holes, a relationship validated experimentally. Notably, observed asymmetry in the waveform was attributed to skin drag effects, and this hypothesis was experimentally verified. Our model computes a solution in less than half a second on average: far less than the 21h 47min needed for a k−ω turbulent model to compute the same phenomenon. The research presents and verifies a simplified model of acoustic mechanics for the sound generated by rotating systems that require little computational resources, which can prove useful in situations where absolute precision is not required, in exchange for ease of computation. For more precise systems, this model serves as a foundation for quickly generating an initial design, paving the way for subsequent iterations using more comprehensive models. The developed model not only serves as a foundation for efficient preliminary designs but also contributes valuable insights into the intersection of fluid dynamics and sound production.