In this article, we examined how linear algebra and bra-ket notation bring quantum states, measurement, time evolution, and entanglement together within a unified mathematical framework.
In this article, we explore the conceptual foundations of quantum mechanics through measurement, reality, the wave function, the EPR–Bell debates, and the key ways in which quantum theory departs from classical physics.
In this article, we introduce a new class of operators, which we call Fractional Sturm–Liouville Operators. Using these operators, we investigate two different classes of Fractional Sturm–Liouville Problems, namely the regular and singular cases.
In this part, we discuss the expansion of the universe, the concept of physical distance, and how distances are defined in cosmology using comoving observers.
In this part, we discuss the historical development of resurgence theory, the Airy function, the Stokes phenomenon, asymptotic analysis, and its applications in quantum mechanics.
In this part, we reduce the hydrogen-atom problem to a one-particle problem using the reduced-mass approximation. By separating the Schrödinger equation in spherical coordinates, we explain the origin of the principal, orbital, and magnetic quantum numbers, energy quantization, orbital shapes, the most probable electron distance, energy degeneracy, and the space quantization of angular momentum.
In this part, we examine the electron's energy-momentum relation in three-dimensional crystal structures of solids using E-k diagrams, and explain direct/indirect band transitions and the concept of effective mass through GaAs and Si.
In this article, we examine the Higgs mechanism step by step with all its mathematical details, from the Mexican-hat potential and spontaneous symmetry breaking to how the electroweak gauge bosons acquire mass.
In this part, we explain the relationship between electric field and potential, the Laplace and Poisson equations, the method of image charges, and how boundary value problems are solved.
In this article, we explain why the principles of special relativity and causality render single-particle quantum mechanics inadequate, the limits of the Klein–Gordon and Dirac equations, and the birth of quantum field theory.
In this article, to understand why supersymmetry is needed, we examine step by step the Standard Model's Higgs mechanism, the electroweak scale, and the hierarchy problem.
In this part, we explain the mechanical equilibrium that keeps stars from collapsing under their own gravity, the sources of pressure, and the fundamental equation of state of stellar matter.
In this part, we use the Kronig-Penney model to solve the Schrödinger equation for an electron in a periodic potential and explain how the allowed energy bands and forbidden band gaps in solid crystals arise.
In this part, we explain the definition of sequences, arithmetic and geometric sequence structures, and the properties of monotonicity, boundedness, convergence and limits.
In this part, starting from starlight, we explain how to characterize a star through brightness, distance, temperature, color, spectrum and the HR diagram.
In this part, we explain the geometric foundations of classical mechanics: affine spaces, configuration manifolds, and the principle of least action.
In this part, we introduce Python and show how to write your first code.
In this part, we discuss harmonicity and minimality.
In this part, we summarize the quantum mechanics equations we will use in later parts.
In this article, we discuss electrostatics.
In this article, we discuss the Schrödinger equation.
In this part, we discuss the first and second fundamental forms and curvature.
In this part, we answer the questions of what Feynman diagrams are and why they are needed.
In this part, we explain the crystal structures of solids.
In this part, we discuss surfaces.
In this part, we discuss the Frenet frame.
In this part, we discuss torsion and curvature.
In this part, we discuss the history of Euclidean geometry and 3-dimensional Euclidean space.
In this part, we discuss the concept of curves and some of their properties.
In this part, we discuss the Frenet frame of curves.
In this part, we cover vector spaces, inner product spaces and normed spaces.
In this article, we discuss vectors, tensors and relativistic dynamics.
In this article, we discuss Relativistic Dynamics.
In this article, we discuss the history of Differential Geometry.
In this article, we discuss the concept of spacetime and spacetime diagrams.
In this article, we discuss Lorentz contraction and time dilation.
In this article, we introduce the theory of Special Relativity and explain the Lorentz Transformations.
