Author Archives: anuj - Page 7
Relationship Between Measure Theory, Lebesgue Integrals, and Hilbert Spaces
Understanding the Relationship Between Measure Theory, Lebesgue Integrals, and Hilbert Spaces To understand the relationship between measure theory, Lebesgue integrals, and Hilbert spaces, we need to break down each…
Lebesgue Integral Solved Problems
Lebesgue Integral Solved Problems Problem 1: Simple Example of a Lebesgue Integral Problem: Compute the Lebesgue integral of the function f(x) = 2 over the interval using the Lebesgue measure.…
The Separability Problem in Quantum Mechanics for Mixed States
Separability Problem in Quantum Mechanics for Mixed States The **separability problem** in quantum mechanics refers to the task of determining whether a given **mixed quantum state** is **separable** or **entangled**.…
Hawking Radiation, How black holes evaporate
Stephen Hawking's seminal paper on black hole radiation, often referred to as **Hawking Radiation**, explains how black holes, previously thought to only absorb matter and energy, can actually emit radiation…
Bell’s Paper – Section 4 – The Proof
### Section IV: Contradiction (Detailed Explanation) In Section IV, Bell presents the formal proof of why a hidden variable theory cannot reproduce the quantum mechanical predictions for certain measurements on…
Trying to Understand Bell’s EPR Paper
Sections 2 and 3 in the paper - I had some trouble deciphering. ### Section II: Formulation In this section, Bell formulates the Einstein-Podolsky-Rosen (EPR) paradox mathematically. He uses the…
Statistical Mechanics of the early Universe
The early expanding universe, especially in the context of the **Big Bang** and the subsequent evolution, can be described through the framework of **statistical mechanics**. This involves the application of…
Introduce Scattering in Bohm’s EPR Experiment
Introduction In the context of Bohm's version of the EPR (Einstein-Podolsky-Rosen) experiment, two entangled electrons are prepared in a singlet state, meaning their total spin is zero. When these electrons…
Some facts and consequences of the binding energy curve
The binding energy curve is a graph that shows the binding energy per nucleon as a function of the mass number (A) of atomic nuclei. This curve has significant implications…
Particle Trajectory in Curved Space Using Jacobi Equation
To derive the trajectory of a particle in a curved gravitational field using the Hamilton-Jacobi equation, we will follow these steps: 1. **Hamilton-Jacobi Equation**: \ Here, \( S \) is…