Physics · Advanced university
First-order stationary perturbation
Nondegenerate first-order perturbation theory; the perturbation is diagonal in the stated orthonormal basis.
Method and conditions
Nondegenerate first-order perturbation theory; the perturbation is diagonal in the stated orthonormal basis.
ΔE⁽¹⁾ = ⟨n|V|n⟩
Worked examples
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
A nondegenerate unperturbed state has component probabilities 0.4 and 0.6 in a basis where V=diag(-15,0) meV. Calculate its first-order energy correction. Round the final result to 4 decimal places if needed. Answer in meV.
Evaluate the diagonal expectation: 0.4(-15)+(1−0.4)(0) meV. Off-diagonal terms of V vanish.
-6 meV
Try it
A nondegenerate unperturbed state has component probabilities 0.9 and 0.09999999999999998 in a basis where V=diag(1,0) meV. Calculate its first-order energy correction. Round the final result to 4 decimal places if needed. Answer in meV.
A nondegenerate unperturbed state has component probabilities 0.6 and 0.4 in a basis where V=diag(-20,2) meV. Calculate its first-order energy correction. Round the final result to 4 decimal places if needed. Answer in meV.
Check your work
Answers and marking notes
- 0.9 meV
Evaluate the diagonal expectation: 0.9(1)+(1−0.9)(0) meV. Off-diagonal terms of V vanish.
- -11.2 meV
Evaluate the diagonal expectation: 0.6(-20)+(1−0.6)(2) meV. Off-diagonal terms of V vanish.
Further reading and review references
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