  In this article, we discard the bra-ket notation and its correlative
definitions, given by Paul Dirac. The quantum states are only described by the
wave functions. The fundamental concepts and definitions in quantum mechanics
is simplified. The operator, wave functions and square matrix are represented
in the same expression which directly corresponds to the system of equations
without additional introduction of the matrix representation of operator. It
can make us to convert the operator relations into the matrix relations.
According to the relations between the matrices, the matrix elements will be
determined. Furthermore, the first order differential equations will be given
to find the solution of equations. As a result, we unified the descriptions of
the matrix mechanics and the wave mechanics.
