Author Archives: anuj - Page 3
The Universal Wave Function
<!doctype html> The World (Universal) Wave Function The world wave function, also called the universal wave function, is the quantum-mechanical wave function that describes the state of the entire universe…
Partial-Sum Probabilities vs. Bell Correlations
Partial-Sum Probabilities vs. Bell Correlations — Illustrated Partial-Sum Probabilities ⇄ Successive Measurements in Bell Experiments Figure: Left — running-partial-sum Markov transitions; Right — Bell measurement settings and entangled state. (Generated…
Randomy generated numbers – Probability of Running Sums
Draws are independent and uniformly chosen from the set \(\{1,2,\dots,k\}\) (with unlimited repetition). Let \(p(n)\) denote the probability that at some time the running sum equals exactly \(n\). 1. Recurrence…
Perfect Gas with Dipole Moments – what can it model?
Can a Perfect Gas of Dipolar Molecules Model Stars or Planets? Short answer: No — a “perfect gas with N molecules each having a dipole moment p” is not…
Spin versus Angular Momentum
Angular Momentum, Spin, and the Particle in a Box Clarifying Angular Momentum in a Particle in a Box The statement “a particle in a box has no angular momentum” refers…
Is a Space Elevator Feasible?
Is a Space Elevator Feasible? Is a Space Elevator Feasible? Short answer: Not with today’s materials—but theoretically yes, if a breakthrough material emerges. A space elevator is a proposed structure…
Angular momentum for particle in a box
angular momentum energy levels …article-in-a-box/ Energy Levels of a Particle in a Box with Angular Momentum 1. Particle in a 1D Box In 1D, angular momentum doesn’t exist in…
Why are wave functions orthogonal?
Orthogonality of Wavefunctions Why Wavefunctions for Different Energy Levels Are Orthogonal 1. They Come From a Hermitian Operator The time-independent Schrödinger equation is: Ĥ ψ = E ψ Here, Ĥ…
Time Dependence of Quantum Mechanical Operators
Time Dependence of Quantum Mechanical Operators In quantum mechanics, the time dependence of operators depends on which representation (picture) we use — primarily the Schrödinger picture or the Heisenberg picture.…
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…