What do you diagonalise to split a degenerate level?

• The perturbation inside that subspace
• The full Hamiltonian of the universe
• Nothing, splitting needs no math

When does the first-order formula break down?

• When the perturbation is switched off
• When levels stand far apart
• When unperturbed states share an energy

A trial state puts a lower bound on the ground state energy.

Circle one:   True   False

Diagonalising gives two different corrections. What do they mean?

• The calculation failed twice
• The levels merged into one
• The shared level splits into two levels

A perturbation links a degenerate pair. What is your next move?

• Apply the plain first-order formula
• Write its two-by-two matrix in the pair and diagonalise it
• Ignore the perturbation entirely

Two trial states give two upper bounds. Which do you trust more?

• The lower one, since it is tighter
• The higher one, since it is safer
• Neither, bounds are useless

Someone reports a trial energy below the true ground energy. What is wrong?

• Trials often dip below, that is normal
• The ground state moved down
• Nothing can sit below it, so the calculation has an error

A classmate diagonalises the full huge matrix instead of the small subspace block. What would you say?

• The full matrix is always mandatory
• Only the block inside the degenerate subspace is needed
• Diagonalising never helps anywhere