Approximating electron states in a cylindrical quantum wire with an intrinsic inverse parabolic potential
Keywords:Electron states, cylindrical quantum wire, inverse parabolic potential, approximating wave functions
A theoretical investigation on comparison of electron states obtained from the exact wave functions and those obtained from approximate wave functions is presented. The functions used to approximate the exact wave functions are the parabolic and the cosine functions. For this purpose, oscillator strength for optical transitions in a cylindrical quantum wire due to circularly polarized electromagnetic radiation was evaluated using the exact wave functions and compared with those obtained using the approximate wave functions. These calculations were carried out within the effective mass approximation. The approximate wave functions preserve the functional form of the oscillator strength and other quantum mechanical quantities upon which it depends, namely the electron eigen energies and the interaction integral. Although the approximate wave functions preserve the functional form of the quantum quantities successfully, they fall short in producing accurate magnitudes of the quantum mechanical properties, which is apparent for excited states.
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