  Quantum mechanics take the sum of first finite order approximate solutions of
time-dependent perturbation to substitute the exact solution. From the point of
mathematics, it may be correct only in the convergent region of the
time-dependent perturbation series. Where is the convergent region of this
series? Quantum mechanics did not answer this problem. However it is relative
to the question, can we use the Schrodinger equation to describe the transition
processes? So it is the most important unsettling problem of physical theory.
We find out the time-dependent approximate solution for arbitrary and the exact
solution. Then we can prove that: (1) In the neighborhood of the conservation
of energy, the series is divergent. The basic error of quantum mechanics is
using the sum of the first finite orders approximate solutions to substitute
the exact solution in this divergent region. It leads to an infinite error. So
the Fermi golden rule is not a mathematically reasonable inference of the.
Schrodinger equation (2) The transiton probability per unit time deduced from
the exact solution of Schrodinger equation cannot describe the transition
processes. This paper is only a prime discussion.
