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Quantum Engineering Year 1: Quantum Mechanics Core Month 16Day 428

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Year 1·Month 16·Week 2

Day 428: Coulomb Problem Setup

Day 428 of 2,016~8 min read

Learning Objectives

•Write the Hamiltonian for the hydrogen atom
•Separate center-of-mass and relative motion
•Define the reduced mass and its importance
•Express the problem in natural atomic units
•Identify the connection to the classical Kepler problem
•Understand why hydrogen is exactly solvable

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The Two-Body Problem Center-of-Mass Separation The Reduced Mass The Relative Motion Hamiltonian Schrdinger Equation Atomic Units The Bohr Radius The Rydberg Energy Separation in Spherical Coordinates Quantum Computing Connection VQE for Hydrogen Atomic Qubits

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