Step-by-Step Solution of One-Dimensional Quantum-Mechanical Problem in Process of Nano-Technological Educations

摘要

In education process exist a problem of create of ability of establishing of connections between properties of real physical object and mathematical model describing such properties. We propose the solution of this problem which is based on a studying of correlation between physical properties of nano-crystal vanadium dioxide thin films and details of quantum-mechanical model of a one-dimensional chain hydrogen-like atoms describing these properties. The main accent is made here on gradual complication of the description of the semiconductor - metal phase transition at T_c = 68℃ which occurs in nano-crystal grains of VO_2-thin films. Consideration in educational process of the nature of phase transition begins on the solution of one-dimensional quantum-mechanical problem, and comes to end with concept of correlation energy and discussion of Mott-idea about dependence of position of energy zones on their electron occupation.