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L6.2 Degenerate Perturbation Theory: Problem 6.6 Detailed Solution Part (a) 2/2
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Welcome to this detailed solution of Problem 6.6 from David J. Griffiths' Introduction to Quantum Mechanics (2nd Edition). In this video, we'll walk through the problem step by step, exploring the orthogonality of unperturbed states, matrix elements of the perturbation Hamiltonian, and energy shifts.
Problem Statement:
Let the two "good" unperturbed states be:
ψ₀₊ = α₊ψₐ₀ + β₊ψ_b₀,
where α₊ and β₊ are determined (up to normalization) by Equation 6.22 (or Equation 6.24). Show explicitly that:
(a) ψ₀₊ and ψ₀₋ are orthogonal (⟨ψ₀₊|ψ₀₋⟩ = 0);
(b) ⟨ψ₀₊|H'|ψ₀₋⟩ = 0;
(c) ⟨ψ₀₊|H'|ψ₀₊⟩ = E₊¹ with E₊¹ given by Equation 6.27.
Key Concepts Covered:
Quantum Superposition
Orthogonality of Quantum States
Perturbation Theory
Energy Shifts
If you found this video helpful, please give it a thumbs up, subscribe to the channel for more quantum mechanics tutorials, and leave a comment below with any questions or suggestions for future videos!
Welcome to this detailed solution of Problem 6.6 from David J. Griffiths' Introduction to Quantum Mechanics (2nd Edition). In this video, we'll walk through the problem step by step, exploring the orthogonality of unperturbed states, matrix elements of the perturbation Hamiltonian, and energy shifts.
Problem Statement:
Let the two "good" unperturbed states be:
ψ₀₊ = α₊ψₐ₀ + β₊ψ_b₀,
where α₊ and β₊ are determined (up to normalization) by Equation 6.22 (or Equation 6.24). Show explicitly that:
(a) ψ₀₊ and ψ₀₋ are orthogonal (⟨ψ₀₊|ψ₀₋⟩ = 0);
(b) ⟨ψ₀₊|H'|ψ₀₋⟩ = 0;
(c) ⟨ψ₀₊|H'|ψ₀₊⟩ = E₊¹ with E₊¹ given by Equation 6.27.
Key Concepts Covered:
Quantum Superposition
Orthogonality of Quantum States
Perturbation Theory
Energy Shifts
If you found this video helpful, please give it a thumbs up, subscribe to the channel for more quantum mechanics tutorials, and leave a comment below with any questions or suggestions for future videos!
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