Author Archives: anuj - Page 3
Mean Square Fluctuations of Energy (monoatomic gas)
Monoatomic Ideal Gas — Energy Fluctuations & Velocity Probabilities Monoatomic Perfect Gas (N particles) Below are (A) the mean-square fluctuation in energy in the canonical ensemble and (B) the probability…
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.…