# Expectation Values & Measurements

Canonical: https://manyspace.aporia.systems/topics/expectation-values-measurements-phy-qm-109
Updated: 2026-10-13

Physics · Quantum Mechanics · PHY-QM-109

- Difficulty: 4 / 5
- Importance: 4 / 5
- Study time: 6.5–11.5 h

postulates of QM, collapse, compatibility of observables

## Why it matters

The fundamental theory of microscopic systems and the mathematical machinery (linear algebra + probability) made physical; required for chemistry, materials, electronics, and modern tech.

## Where it is used

Semiconductors, lasers, MRI, quantum computing, chemistry, nuclear technology, every modern sensing technology.

## How you know you have learned it

Explain/derive key result from memory + solve 2 non-routine checks.

## What you need first

- [Operators & Observables](https://manyspace.aporia.systems/topics/operators-observables-phy-qm-108) (required)
- [Gaussian Elimination](https://manyspace.aporia.systems/topics/gaussian-elimination-mth-linalg-155) (helpful)
- [Separable & Exact Equations](https://manyspace.aporia.systems/topics/separable-exact-equations-mth-ode-185) (helpful)

## Resources

- Modern Quantum Mechanics — J. J. Sakurai
- Introduction to Quantum Mechanics — David Griffiths
- Principles of Quantum Mechanics — R. Shankar