Author Archives: anuj - Page 10
Quantum Logic Gates and Infinite Number of States
Quantum logic gates are created from superposition of spin states. Should't there be an infinite number of possible directions that the spin can point to - so an infinite number…
Complex fourier transform and Wave Packets
Constructing a wave that is spiked in just one small region is not easy. When you superpose several waves, you have to do so in a way that they constructively…
State of an atom after passing through three Stern Gerlach Analyzers Successively
Two SG Detectors - at 90 degrees to each other. First one (SG oriented along z axis) - exiting atom is +m (z axis) (or -m on the z axis).…
Abelain Group
Z(p∞) = { z ∈ ℂ | zpk = 1 for some integer k ≥ 1 } Proof that Z(p∞) is an Abelian Group We define the set: Z(p∞) =…
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…