In this situation, the SE is given by the form i ℏ ℏ ∂ ∂ ∂ ∂ t Ψ Ψ α α ( r , t ) = H ^ ^ Ψ Ψ α α ( r , t ) = ( − − ℏ ℏ 2 2 m ∇ ∇ 2 + V ( r ) ) Ψ Ψ α α ( r , t ) = − − ℏ ℏ 2 2 m ∇ ∇ 2 Ψ Ψ α α ( r , t ) + V ( r ) Ψ Ψ α α ( r , t ) It can be derived from (1) by considering Ψ Ψ α α ( x , t ) := ⟨ ⟨ x | α α ⟩ ⟩ and H ^ ^ := − − ℏ ℏ 2 2 m ∇ ∇ 2 + V ^ ^