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Quantum Engineering Year 1: Quantum Mechanics Core Month 17Day 451

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Year 1·Month 17·Week 1

Day 451: Degenerate Perturbation Theory I

Day 451 of 2,016~3 min read

Learning Objectives

•Identify when degeneracy is a problem
•Set up the secular equation
•Diagonalize H' in the degenerate subspace
•Find the lifted energies to first order
•Determine the "good" zeroth-order states
•Apply to 2-fold degeneracy

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The Problem The Solution Setup for g-fold Degeneracy The Secular Equation First-Order Energies Good Zeroth-Order States Two-Fold Degeneracy Degeneracy Lifting Quantum Computing Connection Avoided Level Crossings Worked Example

Day 450Day 451 of 2,016Day 452