Archives for Basic Quantum Theory
Wave nature and speed of proton (particle)
High-Speed Protons and de Broglie Waves If a proton is moving at high speed, does it affect its de Broglie wave nature? Answer: Yes. A proton always has a wave…
The Universal Wave Function
World / Universal Wave Function — Explanatory Article The World (Universal) Wave Function The world wave function, also called the universal wave function, is the quantum-mechanical wave function that describes…
Spin versus Angular Momentum
Angular Momentum, Spin, and the Particle in a Box Clarifying Angular Momentum in a Particle in a Box The statement “a particle in a box has no angular momentum” refers…
Angular momentum for particle in a box
angular momentum energy levels …article-in-a-box/ Energy Levels of a Particle in a Box with Angular Momentum 1. Particle in a 1D Box In 1D, angular momentum doesn’t exist in…
Why are wave functions orthogonal?
Orthogonality of Wavefunctions Why Wavefunctions for Different Energy Levels Are Orthogonal 1. They Come From a Hermitian Operator The time-independent Schrödinger equation is: Ĥ ψ = E ψ Here, Ĥ…
Time Dependence of Quantum Mechanical Operators
Time Dependence of Quantum Mechanical Operators In quantum mechanics, the time dependence of operators depends on which representation (picture) we use — primarily the Schrödinger picture or the Heisenberg picture.…
The Simple Step Potential and How it Explains the All Paths Feynman Approach
The Simple Step Potential and How it Explains the All Paths Feynman Approach to the Double Slit results It took me forever to understand why we could just 'take all…
Deriving Uncertainty from the Position Operator in p-space
Position Operator in Momentum Space and Uncertainty Position Operator in Momentum Space and the Uncertainty Relation In 1D momentum space the position and momentum operators act very differently: Momentum operator:…
Choosing the Axis to Measure Spin
Spin-½ measurement along a rotated axis (Pauli-matrix derivation) Spin-½ measurement along a rotated axis (Pauli-matrix derivation) We will show explicitly—using Pauli matrices—why a spin-½ measurement along any direction still yields…
Slow Moving vs Fast Moving Electrons – Photon Interaction
Electron–Photon Interaction: Slow vs Fast Electrons Is There a Difference Between a Slow-Moving and a Fast-Moving Electron Interacting with a Photon? Yes — the interaction depends strongly on the electron’s…