Archives for Basic Quantum Theory - Page 3
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,…
Electron interacts with a photon – Schrodinger equation and it’s solution
Schrödinger Equation for Electron-Photon Interaction The system includes: An electron with wavefunction ψe(r, t), A photon field described by the vector potential A(r, t). The total Hamiltonian includes: The electron's…
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…
Feynman’s paths and bohm’s paths in quantum theory
A recap of the Article - Bohm and Feynman Path Integrals - author - Marius Oltean, U Waterloo. Feynman's Path Integral Feynman's approach to quantum mechanics involves the concept of…