  An exact solution of the energy shift in each quantum mechanical energy
levels in a one dimensional symmetrical linear harmonic oscillator has been
investigated. The solution we have used here is firstly derived by manipulating
Schrodinger differential equation to be confluent hypergeometric differential
equation. The final exact numerical results of the energy shifts are then found
by calculating the final analytical solution of the confluent hypergeometric
equation with the use of a software (Mathcad Plus 6.0) or a program programmed
by using Turbo Pascal 7.0. We find that the results of the energy shift in our
exact solution method are almost the same as that in Barton et. al.
approximation method. Thus, the approximation constants (obliquity factors)
appeared in Barton et. al. method can also be calculated using the results of
the exact method.
