Archives for Basic Quantum Theory - Page 5
Example of observables for the EPR paradox – using 2 free non-interacting particles
EPR Argument with Two Pairs of Observables The EPR argument suggests that if we can measure two different pairs of observables and determine the values of one observable from each…
2 free non interacting particles and the EPR paradox
EPR Paradox for Two Non-Interacting Particles The EPR paradox (named after Einstein, Podolsky, and Rosen) arises when considering quantum entanglement and the nature of reality. It challenges the completeness of…
Two free non-interacting particles
Two Non Interacting Particles? It is possible to construct a two-particle wave function for non-interacting particles. The total wave function is simply the product of the individual wave functions in…
Free Particle wave function in momentum eigenstates
Free Particle Wave Function The free-particle wave function can be expressed as an integral over momentum space: ψ(x,t) = (1/√(2πħ)) ∫-∞∞ ψ̃(p) ei(px - Et)/ħ dp where ψ̃(p) is the…
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).…
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…
Finite Abelian Groups and Applications to Quantum Physics
Finite Abelian Groups and Applications to Quantum Physics What Are Finite Abelian Groups? A finite abelian group is a group \( G \) with the following properties: Closure: For any…
Trajectories don’t exist
One of Heisenberg's greatest triumphs was simply eliminating the whole thought process around classical electron trajectories. He claimed that there are only observable quantities - and these quantities can be…
Dipole Approximation in Electron-Photon Interaction
Dipole Approximation for Electron-Photon Interaction The dipole approximation assumes that the wavelength of the electromagnetic field is much larger than the spatial extent of the electron wavefunction. In this case,…