bsc-i
16 Jul 2025
5 min read
Relativistic Doppler Effect
Longitudinal, angular, and transverse relativistic Doppler shifts with explicit sign and angle conventions.
Blog Posts 👇
bsc-v
15 Jul 2025
5 min read
Linear, Circular, and Elliptical Polarization
Polarization ellipse derived from orthogonal field components, with linear and circular limits.
bsc-i
13 Jul 2025
5 min read
Relativistic Mass, Mass–Energy Equivalence, and Massless Particles
Momentum-based derivation of velocity-dependent relativistic mass, total energy, rest energy, and the massless energy-momentum relation.
bsc-i
10 Jul 2025
6 min read
Simultaneity, Event Order, and Relativistic Velocity Addition
Relativity of simultaneity, invariant causal order, and velocity transformation derived by differentiating the Lorentz equations.
bsc-i
07 Jul 2025
6 min read
Length Contraction and Time Dilation
Operational definitions of proper time and proper length, followed by complete Lorentz-transformation derivations.
bsc-i
04 Jul 2025
5 min read
Lorentz Transformations from the Light Postulate
A first-principles derivation of the direct and inverse Lorentz transformations and the invariant spacetime interval.
bsc-i
01 Jul 2025
6 min read
Frames, the Michelson–Morley Experiment, and Einstein's Postulates
Inertial and non-inertial frames, the ether-drift test, its null result, and the two postulates of special relativity.
bsc-v
28 Jun 2025
5 min read
Free Gaussian Wave Packet and Momentum Space
A free-particle momentum eigenfunction extends over all space. A localized free particle must therefore be a wave packet: a continuous superpo...
bsc-v
27 Jun 2025
4 min read
Energy-Eigenfunction Expansion and Time Evolution
Let a time-independent Hamiltonian have a complete orthonormal set of discrete energy eigenfunctions,
bsc-v
26 Jun 2025
5 min read
Schrödinger Equations and Stationary States
For a non-relativistic particle in a scalar potential,
