The book contains four chapters. The first one deals with elementary problems of one dimensional quantum mechanics of scalar particles, and their solution is given by much more simpler method than in standard textbooks. Attention should be paid to problems with periodic potentials. In the second chapter methods of one-dimensional quantum mechanics are applied to three-dimensional scattering problems. Here a new approach to the dynamic diffraction theory based on multiple wave scattering method is proposed. Diffraction on a crystalline plane is solved exactly, and is shown to vanish in contradiction with experimental observations. In the third chapter, all the problems of the first one are generalized to spinor particles. The most interesting questions are related to polarization of particles and rotation of polarization by means of radio-frequency fields, which create superpositions of states with different energies and speeds. The fourth chapter is devoted to fundamental questions of quantum mechanics. The theory of "weak measurements" is criticized. Some experiments related to wave packets and to determination of quantization axis of non polarized neutron beams are proposed.