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Journal of Applied Mathematics and Statistical Applications | Volume: 1
August 23-24, 2018 | London, UK
Applied Physics
3
rd
International Conference on
Generation of exact analytic solution of position-dependent mass Schrodinger equation
Hangshadhar Rajbongshi
Nalbari College, India
E
xtended Transformation, a method of mapping a known
system into a new system is applied to generate exact
analytic solution of position-dependent mass Schrodinger
equation. Some exactly solvable potentials are taken
as known systems and the first order transformation is
performed on D-dimensional radial Schrodinger equation
with constant mass providing exactly solvable potentials
equipped with energy eigenvalues and corresponding
wave functions for different choices of mass functions
for each known system. The transformation is performed
on D-dimensional radial position-dependent mass.
Schrodinger equation also where the systems with
mass functions generated in the first order transformation
are taken as known systems. The important fact is that
the solutions which are meant for central potential with
radially symmetric mass functions are fitted for “Zhu and
Kroemer” ordering of ambiguity. Another result is that
all the wave functions corresponding to non-zero energy
eigenvalues are normalizable and the normalizability
condition of the wave functions remains independent of
mass functions. Thirdly, some of the generated potentials
show a family relationship among themselves where
power law potentials also get related to non-power law
potentials and vice versa through the transformation.
e:
hansrajb12345@gmail.com