| Due to their novel physical properties as well as prospective and potential applications, low-dimensional nanostructures and nanostructured materials, sush as superlattices(SLs), quantum wells, wires and dots, have received increasing interests and become one of frontier research topics in condensed matter physics in recent years. Simultaneously, rapid progress in the synthesis and processing of materials with structures on nanometer length scales has caused that kinds of nanoscale devices, specially about single-electrol devices, had been made, which has created a demand for greater scientific understanding of the electric states of nanoscal devices and the physical properties under exteral field. In this thesis, the quantum system of single electron that trap in harmonic-oscillator and antiharmonic-oscillator potential well constructed by magnetic field interacted with adiabatic phase in the low-dimensional quantum wire is investigated. And we obtain the corresponding exact quantum state, by which, we discuss some interesting physical properties of the quantum system, such as the coherent properties and control of wave-packet-train.The thesis consists of four chapters.In chapter one, we introduce the research situation about low-dimensional adiabatic system, general coherent state and some interrelated researchful case of our investigative group. And we briefly introduce the aim and significant about our the thesis.In chapter two, we study the quantum system of single electron that trap in harmonic-oscillator potential well constructed by magnetic field interacted with adiabatic phase in the one-dimensional quantum wire. By the test-function method and choose the suitable time-space variable, we obtain the exact quantum state of the corresponding quantum system. We study the squeezed coherent properties of the electron trpped. We find that the squeezed factor damply change in short time range and periodically vary with time afterward. We also obtain the expectation of the position and momentum, and we find the similar coherent properties, namely the expectation of the position and momentum agree with the corresponding classical results, which embody the classical-quantum correspondence. We calculate the expectation of system energy; and we find that the average energy is composed of classical and quantum parts, which is different from the energy of any known coherent state.At last, we exhibit the cotrolling to the wave-packet-train of electron under the external field. By adjusting the external field parameters, we can well realize the controlling of oscillating amplitudes, period and the centre position of the oscillation.In chapter three, we study coherent state of single electron in anti-harmonic-oscillator potential well constructed by magnetic field under adiabatic condition. By the test-function method, we get exact analytical solution of system and solution's evolution with adiabatic condition, we investigate high and width of wave-packet-train, and time evolution of Gaussian-type wave-packet's probability density by method combined theoretic analysis and numerical calculation, at the same time, We calculate the expectation of system energy, and we find that the average energy is composed of classical and quantum parts. Finally, we can well realize the controlling of movement of wave-packet's centre by adjusting adiabatic parameters.Especially, a series of comparison of character between trapping electron interfered by adiabatic potential and anti-tapped electron was primarily investigated in this chapter, we find some interesting differentiate and relation between them, after comparing the character that the function of centre position of orbit, the function of high and width of wave-packet-train and probability density of Gaussian-type wave-packet evolution with time, respectively.In the last part of the paper, we give a simple summary and discussion to the above-mentioned works. Here, our main works are involved in chapters two and three. |
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