1. A. M. Fink:Math. Soc. Proc.,20, 73 (1969).
2. Strictly speaking,L takes some members of the space out of the space. If, for example, ψ(x)=x(T−x), thenLψ(x)=2, which does not vanish at the end points. However,Lψ(x) can be considered in the space in the sense that it can be expressed as a linear combination of (infinitely many) members of the space (as a Fourier series, for example). This sort of trouble occurs with any unbounded operator in Hilbert space, which is the case of most operators of physical interest.
3. H. H. Aly andF. Odeh:Lett. Nuovo Cimento,2, 193 (1971).
4. T. Y. Wu andT. Ohmura:Quantum Theory of Scattering (Englewood Cliffs, N. J., 1962), p. 94.