Quantum Systems With Constant Potential

Kyu Hwang Yeon, Shou Zhang, Yong Dae Kim +2 more

The quantum harmonic-parabola system, whose potential energy is the negative harmonic potential, is analyzed and applied to the cases of a quantum well, barrier, and periodic lattices. The eigenstate of the quantum Hamiltonian of the harmonic-parabola system is obtained. It is shown that any function may be expanded in terms of the eigenfunctions of the system in a finite interval, and the propagator of the system can be obtained from the eigenfunctions. The energy eigenvalues, uncertainty, and probability density for the first few states are treated for the infinite harmonic-parabola well. The energy eigenvalues and their enumeration, the energy band, and the probability density for the first few states are obtained for a well composed of the parabola and constant potentials. The transmission coefficients and each potential interval dependence are determined for this well and the barrier of the parabola-constant potential structure. Periodic lattices composed of the parabola potential and parabola-constant potentials are constructed, and their dispersion relations, energy states, and bands are obtained.

Lucattilio Tenuta

Zahra Bakhshi, Sare Khoshdooni

Orest Hryhorchak

An analytical solution for a quantum wave impedance in a case of piesewise constant potential was derived. It is in fact an analytical depiction of a well-known iterative method of a quantum wave impedance determination. The expression for a transmission probability as a function of a particle energy for an arbitrary cascad of constant potentials was obtained. The application of obtained results was illustrated on a system of double-well/barrier structures.

Morávek, Petr

Orest Hryhorchak

The method of a determination of a quantum wave impedance for an arbitrary piecewise constant potential was developed. On the base of this method both the well-known iterative formula \cite{Khondker_Khan_Anwar:1988} and alternative ways for a quantum wave impedance calculation were derived. A scattering and a bound state case were considered. The general form of a wave function of bound states for an arbitrary piesewise constant potential was obtained as well as transmission and reflection coefficients in a scattering case. The applying of method was demonstarted on the system of double well/barrier.