CSIR Practice Quiz

Question 1

For a non-degenerate unperturbed eigenstate |n^(0)⟩ of H0 with perturbation H' = λV, what is the correct first-order correction to the energy?

Accepted Answer

E_n^(1) = ⟨n^(0)|V|n^(0)⟩

Question 2

In non-degenerate time-independent perturbation theory, which expression gives the first-order correction to the eigenstate |n^(0)⟩?

Accepted Answer

|n^(1)⟩ = Σ_{m≠n} ⟨m^(0)|V|n^(0)⟩ /(E_n^(0)-E_m^(0)) |m^(0)⟩

Question 3

A perturbation V commutes with H0, and the unperturbed spectrum is non-degenerate. Which statement is correct?

Accepted Answer

The unperturbed eigenstates are also eigenstates of V, so first-order energies are exact and state mixing is absent

Question 4

For a non-degenerate level n, the first-order correction to the expectation value of an operator A (with no explicit λ dependence) is

Accepted Answer

⟨A⟩^(1) = ⟨n^(1)|A|n^(0)⟩ + ⟨n^(0)|A|n^(1)⟩

Question 5

A perturbation V is odd under parity, and |n^(0)⟩ is a non-degenerate eigenstate of H0 with definite parity. What can be said about the first-order energy correction?

Accepted Answer

It must vanish: E_n^(1)=0

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