The following properties of the evolution operator of 1D TNSM hold even for the SEO of the SDEs of arbitrary form. The evolution operator commutes with the operator of the degree of differential forms. As a result, H ^ ^ = H ^ ^ ( dim ⁡ ⁡ X ) ⊕ ⊕ ⋯ ⋯ ⊕ ⊕ H ^ ^ ( 0 ) , where H ^ ^ ( k ) = H ^ ^ | Ω Ω ( k ) and Ω Ω ( n ) ( X ) is the space of differential forms of degree n . Furthermore, due to the presence of TS, Ω Ω ( X ) = H ⊕ ⊕ N ⊕ ⊕ ( d ^ ^ N ) , where H are the supersymmetric eigenstates, θ θ ′ s , non-trivial in de Rham cohomology whereas the rest are the pairs of non-supersymmetric eigenstates of the form | ϑ ϑ ⟩ ⟩ and d ^ ^ | ϑ ϑ ⟩ ⟩ . All supersymmetric eigenstates have exactly zero eigenvalue and, barring accidental situations, all non-supersymmetric states have non-zero eigenvalues. Non-supersymmetric pairs of eigenstates do not contribute to the Witten index, which equals the difference in the numbers of the supersymmetric states of even and odd degrees, W = # # { even θ θ ′ s } − − # # { odd θ θ ′ s } . For compact X , each de Rham cohomology class provides one supersymmetric eigenstate and the Witten index equals the Euler characteristic of the phase space.