The classical form of Z is recovered when the trace is expressed in terms of coherent states and when quantum-mechanical uncertainties in the position and momentum of a particle are regarded as negligible. Formally, using bra–ket notation, one inserts under the trace for each degree of freedom the identity: 1 = ∫ ∫ | x , p ⟩ ⟩ ⟨ ⟨ x , p | d x d p h , where | x, p ⟩ is a normalised Gaussian wavepacket centered at position x and momentum p. Thus Z = ∫ ∫ tr ⁡ ⁡ ( e − − β β H ^ ^ | x , p ⟩ ⟩ ⟨ ⟨ x , p | ) d x d p h = ∫ ∫ ⟨ ⟨ x , p | e − − β β H ^ ^ | x , p ⟩ ⟩ d x d p h . A coherent state is an approximate eigenstate of both operators x ^ ^ and p ^ ^ , hence also of the Hamiltonian Ĥ, with errors of the size of the uncertainties. If Δ x and Δ p can be regarded as zero, the action of Ĥ reduces to multiplication by the classical Hamiltonian, and Z reduces to the classical configuration integral.