Author Archives: anuj - Page 3
Quantum Key Distribution Scheme
BB84 (Bennett–Brassard 1984) and Non-Commuting Observables Charles Bennett’s Quantum Key Distribution (BB84) and the Role of Non-Commuting Observables The BB84 protocol (Bennett–Brassard, 1984) enables two parties, Alice and Bob, to…
Uncountability of (0,1): Cantor’s Diagonal Argument
The Reals in \((0,1)\) Are Not Countably Infinite See also - Cardinality of the Rationals - Positive and Negative included Claim The interval \((0,1)\subset \mathbb{R}\) is uncountable. Equivalently, there is…
Cardinality of the Rationals (Including Negative Rationals)
Also read 'Cardinality of the Reals' Do Negative Rationals Change the Cardinality? Short answer: No. Adding negative rationals keeps the set countably infinite, the same cardinality as the integers \(\mathbb{Z}\).…
Negative Time Delays and Time Travel Paradox Computational Circuits
Deutsch Circuits with Negative Time Delays & Paradox Resolution Deutsch’s Computational Circuits with Negative Time Delays 1) Context: Computation with Closed Timelike Curves (CTCs) Deutsch (1991) proposed a quantum–mechanical model…
Universal Expansion Clock: Why the Big Bang Was Infinitely Long Ago
Milne’s Expansion Clock: Why the Big Bang Is “Infinitely Long Ago” This explains how, in Milne’s kinematic relativity, using the rate of expansion (or its integral) as the universal clock…
Slow Moving vs Fast Moving Electrons – Photon Interaction
Electron–Photon Interaction: Slow vs Fast Electrons Is There a Difference Between a Slow-Moving and a Fast-Moving Electron Interacting with a Photon? Yes — the interaction depends strongly on the electron’s…
Particle in an Infinite 1D Square Well — Momentum Distribution
Momentum Distribution for a Particle in an Infinite 1D Well Also read - Particle in a 1-D infinte well - Energy States Setup Infinite well from \(0\) to \(a\). The…
Wave Packet Velocity Derivation
Group and Phase Velocity of a Localized Wave Packet Group and Phase Velocity for a Localized Wave Packet Build a Wave Packet Consider a superposition of plane waves centered near…
Particle in an Infinite 1D Square Well — Energy States
Energy States of a Particle in an Infinite 1D Square Well Setup Consider a well of width \(a\) with potential \ The time-independent Schrödinger equation (TISE) inside the well is…
Particle in a Box? Momentum and Distance Traveled – 1-Inch box to Atomic Scale Box
How “Stationary” Is a Particle in a Box? Momentum and Travel Distance from 1-Inch to Atomic Scales How “Stationary” Is a Particle in a Box? Momentum and Travel Distance from…