Author Archives: anuj - Page 2
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…
Is a Space Elevator Feasible?
Is a Space Elevator Feasible? Is a Space Elevator Feasible? Short answer: Not with today’s materials—but theoretically yes, if a breakthrough material emerges. A space elevator is a proposed structure…
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…
Temporal Green’s Functions
Temporal Green’s Function Temporal Green’s Function The temporal Green’s function is the Green’s function that solves a differential equation involving time — typically the evolution equation of a dynamical system…
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…
Striking of a bell and the sound heard – as per two observers
Relativistic Bullet & Bell — Two Observers Relativistic Bullet Striking a Bell: Frame Analysis Events in the bell’s rest frame \(S\): \(A\): bullet strikes bell at \((t=0,\;x=0)\). \(B\): bell begins…