This page is a map and a promise. It is a guide to how physics is learned and built. It shows how ideas travel from sketches on a notebook to experiments that hum in a lab and to code that searches patterns in numbers. Quantum is a constant thread. The goal is clarity through real inquiry and careful awe.
Every topic on this site fits inside three working modes. Theoretical work builds models and proofs. Experimental work designs instruments and measurements. Computational work uses data and simulation to test and extend both. You can wander or follow a path. The content below offers a structured start.
Theory asks what can be true and still be consistent. Here you will see Lagrangians, operators, spectra, and conservation laws. You will also see simple core ideas. Variation tells us how nature selects a path. Symmetry predicts conservation. Measurement gives probabilities. A short sample appears as
$$ \hat{H} \Psi = E \Psi $$
tags: Hilbert space Noether Spectral theory Information
Open theoreticalExperiments answer the question what is so. We care about calibration, background, and uncertainty. You will find photodiodes, lock in methods, interferometers, and cryogenic tricks. The focus is on how to turn a signal into a claim with clear limits.
tags: interferometry spectroscopy noise statistics
Open experimentalCode connects equations to numbers and then to pictures that the mind can hold. We use numerical integration, Monte Carlo methods, and simple machine learning when it helps. Reproducible notebooks appear across the site. Clarity first, speed next.
tags: method visualization reproducibility open data
Open computationalThe links below collect pages into short routes. Each route begins simple and grows in precision. You can also open any topic from the menu at the top of the site.
A clear overview of vectors, fields, energy, and symmetry. Why symmetry tells a story about conservation. Why units matter. This section prepares you to read equations with comfort.
Open conceptsDimensional analysis. Order of magnitude estimates. Linearization. These ideas are used by every good physicist in every branch.
See methodsSmall actions yield large structure. From a simple principle we find the Euler Lagrange equation. From invariance we read a conserved quantity. This is the rhythm of theory on QParadox.
L = T - V
d/dt(∂L/∂q̇) - ∂L/∂q = 0
The state as a vector. Observables as operators. Probabilities from inner products. Time evolution from the Hamiltonian.
Superposition. Interference. Entanglement. Collapse as a modeling rule for outcomes. We show the logic with clear pictures and with minimal algebra first.
Complex amplitudes add. Probabilities come from the modulus.
Two paths. A and B.
A = 1 and B = i.
Total amplitude = 1 + i.
Probability = |1 + i|^2 = 2.
Real labs see loss and noise. We talk about visibilities, count rates, and alignment tricks. There is beauty in a clean fringe on a tired afternoon.
Open lab notesA two level system teaches measurement and basis change. It also teaches how to compute quickly.
Read spin notesQuantum states carry limits on knowledge. The information view shows why uncertainty is not a flaw but a rule. It also links physics to computation and to thermodynamics.
See information toolsYou will meet calibration curves, Allan deviation, and simple fitting. The point is to claim only what the data allow. The craft is patient.
Measurement guideA short guide to mirrors, mounts, and alignment. You can run a lab with little money if you think and measure with care.
Bench basicsWhite noise. Flicker noise. Shot noise. Thermal noise. Once you see their shapes you begin to predict them and to design around them.
You will see time stepping, eigenvalue problems, and random sampling. The goal is insight and clean pictures that tell a true story.
// tiny pseudocode
for t in steps:
psi = psi + dt * H(psi)
psi = normalize(psi)
Numerics overview
You will learn to split data into train and test with honest baselines. You will learn to present results with uncertainty bars that mean something.
Data workflowLinear algebra, calculus of variations, complex analysis, and probability. Each topic comes with short primers that you can read in a single sitting.
Open primersPhotodiodes, spectrometers, oscilloscopes, and simple motion stages. You will learn how to select and use them with confidence.
Instrument notesVectors in code, numerical eigen problems, and signal processing. Notebooks show exact steps with explanations in plain words.
Open notebooksHow to form a question. How to decide if a model earns trust. How to explain a result without hype.
Read moreA short reading shows how each symbol in the Schrödinger equation points at a physical act. The constant $\\hbar$ sets the scale of action. The operator $\\hat{H}$ sets how the state drifts in time. The derivative in time tells you the rate of change of probability content across the state.
Swipe or scroll. Each card links to a larger note on the site.
How a drive swaps populations in time. Clear plots and a short derivation.
Open noteHow contrast tells you about mode match and stability in a real setup.
Open noteFrom random walk to estimates with error bars that you can trust.
Open notebookHow spectra carry stories about temperature, motion, and composition.
Open essayA warm up for the mind. No grades. Only curiosity.
Question. A photon counter records an average of four counts per millisecond with Poisson statistics. What is the standard deviation per millisecond
QParadox is written by a student who studies with care and joy. The intent is to be rigorous and also human. Every page tries to explain the thing itself and not only the symbol that names it. No part of physics is treated as a puzzle box for insiders. You will find proofs and measurements and also quiet lines that speak about meaning. The world is lawful and also surprising. That mix is the reason this project exists.
Try a few. These tiny notes appear across the site. They invite careful reading without breaking the flow.
Hilbert space gives the stage for quantum states.
Conserved quantity is a gift from symmetry.
Poisson process is the natural model for count events in time.