I recently added a custom Fortran syntax highlighting function to the libraries I develop. This feature focuses on enhancing the readability of Fortran code by wrapping key constructs with distinct CSS classes for visual clarity. In addition to handling traditional Fortran comments and data types, my approach also highlights string literals, numbers, and mathematical operators, ensuring that both F77 and F90 styles are supported. This addition significantly improves code clarity, particularly for complex scientific and engineering computations where Fortran is widely used.
I recently added a custom C++ syntax highlighting function to the libraries I develop, aimed at improving code readability for key elements such as types, strings, and control flow. The approach automatically wraps matching tokens and string literals with specific CSS classes for easy identification. My method goes beyond just simple keywords by also identifying format specifiers within strings and handling both single-line and multi-line comments.
電子ビームが二重スリット障壁を通過するシミュレーションを完了し、波動-粒子二重性を実証しました。このシミュレーションは２Ｄシュレーディンガー方程式のソルバーに基づいており、波束の伝播、スリットを超えたスクリーン上の確率密度の蓄積、電子の衝突パターンの可視化という3つの部分で構成されています。シミュレーションは干渉パターンを捉え、電子の数が１５，０００から１５０，０００に増えると、干渉縞がより鮮明になり、全体的な分布を変えることなく波動-粒子二重性をより明確に示しています。
Ho completato una simulazione del fascio di elettroni attraverso una barriera a doppia fenditura, dimostrando la dualità onda-particella. La simulazione, basata su un risolutore dell'equazione di Schrödinger 2D, comprende tre parti, propagazione del pacchetto d'onda, accumulo della densità di probabilità su uno schermo oltre le fenditure e visualizzazione degli impatti degli elettroni. La simulazione cattura il modello di interferenza, con frange che diventano più definite man mano che il numero di elettroni aumenta da 15.000 a 150.000, evidenziando chiaramente la dualità onda-particella senza alterare la distribuzione complessiva.
I completed an electron beam simulation through a double-slit barrier, demonstrating wave-particle duality. The simulation, built on a 2D Schrödinger equation solver, includes three parts, wavepacket propagation, probability density accumulation on a screen beyond the slits, and visualization of electron impacts. The simulation captures the interference pattern, with fringes becoming sharper as the number of electrons increases from 15,000 to 150,000, showcasing clearer wave-particle duality without altering the overall distribution.
In the final step of my electron double-slit experiment simulation, I model the collapse of the wavefunction and simulate the electron beam impacting the screen. After normalizing the probability distribution, I compute the positions where individual electrons strike the screen based on this distribution. By randomly selecting regions on the screen according to the computed probabilities, I simulate the detection of thousands of electrons. The result is a visualization of the interference pattern, where the accumulation of electron impacts aligns with the expected quantum mechanical behavior. I further visualize the pattern through both scatter and line plots.
In the second part of my electron double-slit experiment simulation, I focus on the accumulation of probability density on a screen that simulates the impact of electrons. Using a predefined screen position, I compute which cells on the grid are crossed by the electron's wavepacket, adapting Bresenham's algorithm for efficient tracking. Once the grid cells are identified, I calculate the probability density or the wavefunction modulus at each cell for every time snapshot. This data is accumulated over time, allowing visualization of the interference pattern as electrons are detected on the screen.
In my latest work, I present a simulation of the electron double-slit experiment to showcase the quantum mechanical nature of electrons. Using a 2D Schrödinger equation, I model the propagation of an electron wavepacket through a double slit, tracking its probability density and visualizing the resulting interference pattern. This article outlines how I numerically solved the time-dependent Schrödinger equation, included a customizable slit setup, and accumulated the wavepacket's probability distribution. With this simulation, I aim to demonstrate the key principles of quantum interference and wave-particle duality inherent in electron behavior.
In this post, I explored the concept of reducing a system of coplanar forces to a single resultant force, illustrating the process with detailed calculations and practical examples. By computing the resultant force and the moment about a specific point, I determined the line of action for the resultant, ensuring the system's equilibrium. This approach is crucial for simplifying complex force systems, making it easier to analyze the effects on a body within the same plane. Through this example, I demonstrated the precision required in determining the correct line of action to maintain the desired moment.
In my latest exploration of static equilibrium in rigid body mechanics, I focus on the fundamental conditions required to maintain balance in both two and three dimensions. By applying the principles of transmissibility and understanding equivalent systems, I demonstrate how forces and moments can be analyzed to ensure an object remains stationary. Using a practical example, I illustrate how to find equivalent force systems and moments, emphasizing the critical role these concepts play in advanced mechanics.
In this article, I explore the concept of the moment of a force, also known as torque, which measures the tendency of a force to cause rotation about a point or axis. Starting with the fundamental cross product between the position vector and force vector, I illustrate how to calculate the moment in both two-dimensional and three-dimensional systems. I also explain Varignon's Theorem and its application in simplifying complex problems, as well as the moment of a force about a line and the special case of a couple.
In this article, I examine the behavior of a beam splitter when interacting with multimode quasi-classical states, focusing on both single and double detection in the output channels. Using Heisenberg formalism, I analyze the propagation of quasi-classical wavepackets and derive the probabilities of detection in each mode. I also explore the quantum mechanical implications of two-photon states at the beam splitter, comparing classical intuition with results from quantum optics. The outcomes of this study reveal fundamental insights into photon distribution across output channels, consistent with both theory and experimental validation. This work has applications in quantum physics and photonics.
In this post, I discuss the essential differences between scalars, vectors, and forces, and how they play a crucial role in understanding mechanical equilibrium. Scalars are quantities defined by magnitude alone, while vectors include both magnitude and direction. Forces, being vectors, influence the motion and acceleration of objects. I explain the conditions for static equilibrium, where the sum of all forces acting on a body must be zero. I also provide examples of force equilibrium in both Cartesian and polar coordinate systems, offering insight into how these principles apply in mechanical engineering and physics.
In this article, I explore the mathematical framework behind collimated quasi-classical wavepackets propagating along a single axis with negligible diffraction. By defining the wavepacket as a product of plane-wave modes around a central frequency, I derive expressions for the photon number distribution and compute the electric field's classical expectation value. This leads to a concise formula for the photodetection rate, which accounts for the quantum state's quasi-classical nature. Finally, I demonstrate that the double photo-detection probability is non-zero, even when the average photon number is small, aligning with experimental results from quantum optics.
In my recent work, I explore the mathematical structure and physical implications of multimode quasi-classical states in quantum systems. These states are represented as a tensor product of quasi-classical states across multiple modes. I also investigate how the detection rates of the electric field correspond to classical fields and derive the variance and distribution of photon numbers, demonstrating that they follow a Poisson distribution. Through the use of creation and annihilation operators, I develop a framework to describe multimode states, providing insights into photon behavior in multimode quantum fields.