Working from the definition, a partial solution for a wavefunction of a particle with a constant energy can be constructed. If the wavefunction is assumed to be separable, then the time dependence can be stated as e − − i E t / ℏ ℏ , where E is the constant energy. In full, Ψ Ψ ( r , t ) = ψ ψ ( r ) e − − i E t / ℏ ℏ where ψ ψ ( r ) is the partial solution of the wavefunction dependent on position. Applying the energy operator, we have E ^ ^ Ψ Ψ ( r , t ) = i ℏ ℏ ∂ ∂ ∂ ∂ t ψ ψ ( r ) e − − i E t / ℏ ℏ = i ℏ ℏ ( − − i E ℏ ℏ ) ψ ψ ( r ) e − − i E t / ℏ ℏ = E ψ ψ ( r ) e − − i E t / ℏ ℏ = E Ψ Ψ ( r , t ) . This is also known as the stationary state, and can be used to analyse the time-independent Schrödinger equation : E Ψ Ψ ( r , t ) = H ^ ^ Ψ Ψ ( r , t ) where E is an eigenvalue of energy.