Modern heterostructure devices as esgc heterojunctions, sing.le quantum wells, and s+erlattices are often isotropic in one plane s o that effectively a onedimensional problem remains only. Therefore exact solutions of the one-dimensional SchrBdinger equation and their properties are of fundamental interest. In recent times the continuum states play an essential role, especially in resonant tunneling structures /1 t o 4/. In these calculations the infinite space is usually preferred rather than the large box quantization because the handling of the former one is easier. But, on the other hand, the powerful results concerning (regular ) Sturm-Liouville problems /5/ a r e not applicable, and one has t o resort to the more elaborate theories of Weyl, Titchmarsh, and Kodaira /6 t o 8/. But the additional suppositions on the potential (continuity o r absolute integrability) often made in these theories are sometimes not satisfied by the model systems which are studied in the applications mentioned above.Because there were controversial discussions regarding the normalization, orthogonality, and completeness of eigenfunctions in the infinite space /2, 4, 9/ we will treat these problems for a finite step potential explicitly. The restriction t o this potential is caused by brevity; a generalization t o more complicated quantum well o r quantum b a r r i e r structures and/or the inclusion of Ben Daniel-Duke Hamiltonians /lo/ with a stepwise constant potential is straightforward. (For instance, one can prove completeness for the potential (6) of /4/ with only slight modifications of the procedure described in the following.) F o r potentials with bound states one has t o take into account these onea in the contour integration (see below) in such a way as in /ll/-Our model system is Hy&)= %*(d 1) PSF 327, DDR-6300 Ilmenau, GDR.

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It is well known that ℳn, the multiplicative group n consisting of n-rowed square matrices with integer entries and determinant equal to ±1 can be generated by:It is also known that U4 can be generated by U1, U2, and U3 (cf.[2] p.85).However, by a construction which is much simpler than the one just mentioned for U4, it is possible to generate U3 by just U2 and U4. Since U2 and U4 affect only the first

In their classic treatment (5) Veblen and Young build n-dimensional projective geometry from points and lines. Naturally, each line becomes identified with the set of points with which it is incident, and many treatments build from points alone, postulating the existence of certain distinguished subsets of the set of points. From either point of view, some labour is required, even in the two-dimensional case, to establish duality; hence a considerable interest attaches to self-dual systems of axioms; cf. (2; 3).