Archives for Basic Quantum Theory - Page 2
The Simple Step Potential and How it Explains the All Paths Feynman Approach
The Simple Step Potential and How it Explains the All Paths Feynman Approach to the Double Slit results It took me forever to understand why we could just 'take all…
Deriving Uncertainty from the Position Operator in p-space
Position Operator in Momentum Space and Uncertainty Position Operator in Momentum Space and the Uncertainty Relation In 1D momentum space the position and momentum operators act very differently: Momentum operator:…
Choosing the Axis to Measure Spin
Spin-½ measurement along a rotated axis (Pauli-matrix derivation) Spin-½ measurement along a rotated axis (Pauli-matrix derivation) We will show explicitly—using Pauli matrices—why a spin-½ measurement along any direction still yields…
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…
Momentum Space Representation of the 1\r Operator
Momentum Space Representation of the \( \frac{1}{r} \) Operator The operator \( \frac{1}{r}, \quad r = |\mathbf{x}| \) plays a central role in quantum mechanics, especially in Coulomb potentials,…
Estimate the nuclear radius size based on Electrostatic and Magnetic Field Strengths
The Rasetti–Fermi Paradox: Electrostatic vs. Magnetic Radius of the Nucleus The Rasetti–Fermi Paradox (1926–1927): Two “Radius” Estimates That Don’t Match A historical back-of-the-envelope puzzle: estimating a nuclear “radius” from an…