Author Archives: anuj - Page 2
HR Diagrams for stellar evolution
HR diagram Hertzsprung-Russell (HR) Diagram The Hertzsprung-Russell (HR) diagram is a key tool in astrophysics used to classify stars based on their luminosity, spectral type, color, temperature, and evolutionary stage.…
Projection Operators and Hidden Variables in QM
Gleason’s Theorem and Hidden Variables 1. Projection Operators A projection operator \( P \) is a Hermitian operator satisfying: P² = P These operators represent measurement outcomes in quantum…
Hidden Variables in Quantum Mechanics and Bell’s Rebuttal
Hidden Variables in Quantum Mechanics The Hidden Variables section in Ballentine's Statistical Interpretation of Quantum Mechanics examines the possibility of supplementing quantum mechanics with additional parameters (hidden variables) that determine…
Joint Probability Distributions in Ballentine’s Statistical Interpretation of Quantum Mechanics
Joint Probability Distributions in Quantum Mechanics Key Points: 1. Marginal Distributions Must Agree with Quantum Theory The joint probability distribution must reproduce the standard quantum probability distributions when integrated over…
Delta p = infinity does not mean momentum is infinite
Understanding Infinite Uncertainty in Momentum When Δp = ∞, it means that the uncertainty in momentum is infinitely large, not that the actual momentum itself is infinite. This distinction is…
Spin States are not a function of space
Spin Angular Momentum Definition For a spin-1/2 particle, spin operators are represented by the Pauli matrices: S_x = (ħ/2) σ_x, S_y = (ħ/2) σ_y, S_z = (ħ/2) σ_z where σ_x…
Momentum Expectation value for a free particle
Expectation Value of Momentum for a Free Particle The expectation value of the momentum operator \( \hat{p} = -i\hbar \frac{\partial}{\partial x} \) is given by: \ By expressing the…
Hydrogen Atom Stationary States Calculation
Hydrogen Atom in 1D: Schrödinger Equation Solution Step 1: Time-Independent Schrödinger Equation (TISE) The 1D Schrödinger equation for a hydrogen-like atom is: \ Step 2: Change of Variables Using…
Derivation of the Classical and Quantum Correlation Functions in EPR , Bell’s Theorem
Derivation of Correlation Functions Hidden Variable Theory Correlation In a local hidden variable (LHV) theory, measurement results depend on pre-existing hidden variables (denoted λ) rather than quantum superposition. Each particle…
Quantum Mechanical Correlation in Bell’s Theorem
Quantum Correlations and Hidden Variable Predictions 1. Correlations Predicted by Quantum Mechanics For two entangled spin-1/2 particles, the quantum state is: |ψ⟩ = (1/√2) ( |↑⟩₁ |↓⟩₂ - |↓⟩₁ |↑⟩₂…