We present direct measurements at room temperature of the conductance
of a point contact between a scanning tunneling microscope tip and Ni,
Cu, and Pt surfaces. As the contact is stretched the conductance jump
s in units of 2e2/h. Atomistic simulations of the stretch of the conta
ct combined with calculations of the conductance using the Landauer fo
rmula show that the observed behavior is due to the quantization of th
e transverse electron motion in a contact which contains between one a
nd ten atoms.