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Quantum Engineering Year 1: Quantum Mechanics Core Month 13Day 337

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Year 1·Month 13·Week 1

Day 337: Complex Vector Spaces — The Arena of Quantum Mechanics

Day 337 of 2,016~11 min read

Learning Objectives

•Define a complex vector space and verify the axioms
•Understand why quantum mechanics requires complex numbers
•Work with finite and infinite-dimensional vector spaces
•Define linear independence, span, basis, and dimension
•Express quantum states as vectors in abstract spaces
•Connect abstract formalism to wave functions

Today's Schedule (7 hours)

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On this page

1 Why Complex Vector Spaces 2 Definition of a Vector Space 3 Examples of Vector Spaces in Physics Example 1 Finite-Dimensional Example 2 L Infinite-Dimensional Example 3 Countably Infinite 4 Linear Independence and Span 5 The Superposition Principle 6 From Abstract to Concrete Wave Functions 7 The Quantum State Postulate Physical Interpretation Why Vectors The Two-Slit Experiment

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