A new approach to derive the Landauer formula is developed by treating
the current flowing ballistic conducting channel as an open system, i
n which an electronic distribution function shifts in proportion to an
external current flow. The effect of an open system is taken into acc
ount by means of the Lagrange multiplier. By introducing current refle
ction and transmission coefficients, and by explicitly treating the vo
ltage drop under the condition that the contact between the lead and t
he electrode is ideal, two types of circuit equations corresponding to
two Landauer formulas are obtained. In our analysis, the Landauer for
mula is not reproduced when there are no scattering centers in each le
ad, i.e., each lead is ideal, but is reproduced when there is no elast
ic scattering and the phase coherence is lost in each lead.