### Tag: Full math

Quantum uncertainty is not caused by measurements

## Quantum uncertainty is not caused by measurements

TL;DR – The uncertainty relationship in quantum mechanics exists before and independently of measurements. Some books still perpetuate the idea that the uncertainty introduced by quantum mechanics is caused by measurements. Either as an observer effect (i.e. the measurement causes the uncertainty) or as an observed relationship (i.e. our measurements are limited by that relationships). …

Determinism and quantum mechanics

## Determinism and quantum mechanics

TL;DR – The Schrodinger equation can be seen as the deterministic and reversible limit of the projection (i.e. collapse) associated with a measurement. Quantum mechanics comes with two ways to go from an initial to a final state. The first is the Schrodinger equation that represents time evolution and the second is the projection (or …

All quantum states are equally defined

## All quantum states are equally defined

TL;DR – No quantum state is more uncertain than the other. All states can be identified by a set of perfectly prepared quantities. When studying quantum mechanics, you may get the (wrong) impression that some states are better defined than others. Some are eigenstates while others are just a superposition. Or that the gaussian packets, …

What are commutators?

## What are commutators?

TL;DR – Commutators, like Poisson bracket, tell us how a quantity changes under a transformation generated by another. Commutators play a fundamental role in quantum mechanics. Mathematically, they tell us how multiplication between operators behaves but this does not provide any physical insight. What is more interesting physically is that they are intimately related to …

Not everything we measure is an eigenvalue of a linear operator

## Not everything we measure is an eigenvalue of a linear operator

TL;DR – Statistical quantities (e.g. averages) and angles (e.g. direction of spin) are measurable quantities but are not associated with linear operators, eigenkets and eigenvalues. When studying quantum mechanics you learn about observables, how to each you associate a Hermitian operator, how the value is only defined on the eigenstates of that operator and how, …