Physics · Advanced university
First-order stationary perturbation · formula reference
Nondegenerate first-order perturbation theory; the perturbation is diagonal in the stated orthonormal basis.
Formula
Nondegenerate first-order perturbation theory; the perturbation is diagonal in the stated orthonormal basis.
ΔE⁽¹⁾ = ⟨n|V|n⟩
Worked example
A nondegenerate unperturbed state has component probabilities 0.9 and 0.09999999999999998 in a basis where V=diag(8,-11) meV. Calculate its first-order energy correction. Round the final result to 4 decimal places if needed. Answer in meV.
Evaluate the diagonal expectation: 0.9(8)+(1−0.9)(-11) meV. Off-diagonal terms of V vanish.
6.1 meV
Prerequisites and checking
Algebra, calculus and the stated physical model. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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