The variational method shows that if the single-particle wavefunction satisfies the following Gross–Pitaevskii equation ( − − ℏ ℏ 2 2 m ∂ ∂ 2 ∂ ∂ r 2 + V ( r ) + 4 π π ℏ ℏ 2 a s m | ψ ψ ( r ) | 2 ) ψ ψ ( r ) = μ μ ψ ψ ( r ) , the total wave-function minimizes the expectation value of the model Hamiltonian under normalization condition ∫ ∫ d V | Ψ Ψ | 2 = N . Therefore, such single-particle wavefunction describes the ground state of the system.