Ladder Operators and Coherent States for Electrons Under Double Parabolic Confinement in a Quantum Wire

Year 2016, Volume: 12 Issue: 3, 427 - 435, 26.12.2016

Mustafa Kemal Bahar

Abstract

In
this study, we have chosen the spatial confinement parabolic on semiconductor
quantum wire with applied magnetic field. Thus, electrons are confined in zone
where two parabola overlapped by using single step between two parabolic
potential. The energy eigenvalues and wave functions of electrons under this
double parabolic confinement are obtained by solving Schrödinger equation in
the framework of asymptotic iteration method. The creation and annihilation
operators for the radial wave functions are constructed by using factorization
method, it is shown that these ladder operators satisfy the commutation
relations for the SU(1,1) group. Closed analytical expressions for the matrix
elements of  and  are
obtained and the coherent state analysis for the system are carried out.

Keywords

SU(1, 1) groups, ladder operators, coherent state, matrix elements, quantum wire

References

• Cooper, I.L. An Integrated Approach to Ladder and Shift Operators for The Morse Oscillator, Radial Coulomb and Radial Oscillator potentials. J. Phys. A: Math. Gen. 1993; 26, 1601-1623.