No abstract

Every physicist interested in nonrelativistic wave mechanics can now gain a deeper insight into quantum intuition. This is possible thanks to the advance in the theories of the inverse problem and supersymmetry which provides numerous new classes of exactly solvable models and instructive and clear illustrations revealing the fundamental elements of the coupling between potentials and observables; how to change the disposition of bound states on the energy scale (to shift, create or destroy the spectral levels) and in space by a special choice of potential perturbation. This theory explains the algorithms to control scattering features and wave motion over the lattices (e.g. crystal or discrete variable numbering channels). The best of thousands of corresponding 'quantum pictures' are selected here. The predictive power of the acquired intuition allows us to go beyond the scope of the exact models used for its elaboration.

A quantum-mechanical problem about the penetration through the potentical barrier of two particles in mutual bound state (complex particle) is considered. The account of the internal structure of a complex particle leads to a spreading of the potential barrier which facilitates the penetration through this barrier.The Hamilbonian of the system of two particles interacting with each other by means of the potential v12(x! -x2) and moving in the external field vl(yl) which affects t.he particle 1 (the influence of the external field upon both particles is considered in a similar way) reads: 2m, 2nPWe consider the case when v12 (xl -x2) is an infinite square potential well :Let a potential acting on the first particle be of the form of a rectangular barrier with the hight V, 0 if xi < a and xl> bIn what follows it will be more convenient to use not the coordinates xi and x2 of particles but bhe coordinates of the relative distance of particles e and of their cent.er of mass RIn terms of the coordinates xi and x2 the region in which particles are moving looks like that represented in Fig. 1. The particles cannot go away from each other a t a distance larger than r. Therefore in the plane (xi x2) we shall be interested only in the band which lies between the straight lines A B and CD.In going over to the coordinates R and e the whole picture (Fig. 1) turns and the band ABCD takes the horizantal position (Fig. 2.) 16 Ann. Physik. 7. Folge. Bd. 14

No abstract

No abstract