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Quantum Engineering Year 1: Quantum Mechanics Core Month 13Day 338

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Year 1·Month 13·Week 1

Day 338: Dirac Notation — The Language of Quantum Mechanics

Day 338 of 2,016~9 min read

Learning Objectives

•Write quantum states in Dirac bra-ket notation
•Compute inner products using bracket notation
•Construct outer products |ψ⟩⟨φ|
•Compute matrix elements ⟨φ|Â|ψ⟩
•Use the dual correspondence between bras and kets
•Express operators in terms of outer products

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1 The Genius of Dirac Notation 2 Kets State Vectors 3 Bras Dual Vectors 4 Brackets Inner Products 5 Outer Products Operators 6 The Completeness Relation 7 Matrix Elements 8 Adjoint in Dirac Notation Physical Interpretation Probability Amplitude Transition Amplitude Expectation Value

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