New wavefunctions for the excited states of an axial impurity in a quantum wire

Abstract

The binding energy of a central hydrogenic impurity located in a finite confining potential quantum well wire (QWW) has been calculated within the effective mass approximation. The study is devoted to deal with the first four excited states (2P±, 2Pz and 2s) in the presence of a uniform axial magnetic field. The different effective masses of the wire and barrier are taken into consideration. New forms of the trial variational wavefunctions have been introduced. These forms are analogous to the new form given in our earlier work on the ground state (1s). They are distinct from the conventional forms by the fact that they satisfy the required boundary conditions in the case of different masses of wire and barrier. The resulting new expressions for the energy and binding energy of the four excited states have led to more accurate results for the binding energy and have improved considerably its values. It is also of importance to point out that a new iteration technique has been introduced to perform the minimization procedure for the energy of the state (2s). This technique may be applied in similar problems of slow convergence.