Archives for February, 2025
Examples of Taylor SEries versus Fourier Series
Intro Which works better for a given function - a Taylor expansion or a Fourier Expansion? This post explores the pros and cons of each, using specific examples. Examples of…
Taylor Series versus Fourier Series for a function
. Domain of Representation Taylor Series: Works best for local approximations around a single point (Maclaurin series if centered at zero). Fourier Series: Represents a function over an entire interval…
Neutron Stars and Pulsars – Mathematical Differences
Mathematical Difference: Neutron Star vs Pulsar Neutron Star A neutron star is a highly dense remnant of a massive star after a supernova explosion. It is characterized by: Mass: \(…
Bells’ Theorem and Thermodynamics
Bell’s Theorem and Its Relation to Thermodynamics 1. Fundamental Differences Bell's Theorem: Demonstrates that no local hidden variable theory can fully explain quantum correlations observed in entangled systems. It is…
Non Stationary Spacetime Metric and redshift
Redshift from a Non-Stationary Metric 1. Understanding Redshift from a Non-Stationary Metric The redshift arises because the wavelength of light is stretched as it propagates through a dynamically changing…
Convolution Integrals for Entangled Quantum States
Convolution Integrals in Schrödinger’s Equation for Entangled Systems 1. Green's Functions and Propagators The solution to the time-dependent Schrödinger equation often involves propagators, which describe the evolution of a wavefunction…
Functions ONLY definable by their integrals – with applications
Functions ONLY Defined by Their Integrals 1. The Gamma Function \( \Gamma(x) \) \( \Gamma(x) = \int_0^\infty t^{x-1} e^{-t} \, dt \), for \( x > 0 \). Applications: Generalization…
Functions Defined by Their Integrals – with applications
Functions Defined by Their Integrals Functions that are defined by their integrals often arise in fields like physics, probability theory, and engineering, where the direct formulation of a function may…