Most binocular vision models assume that the two eyes sum incompletely. However, some facilitatory cortical neurons fire for only one eye, but amplify their firing rates if both eyes are stimulated. These ‘binocular gate’ neurons closely resemble subthreshold multisensory neurons. Binocular amplification for binocular gate neurons follows a power law, with a compressive exponent. Unexpectedly, this rule also applies to facilitatory true binocular neurons; although driven by either eye, binocular neurons are well modeled as gated amplifiers of their strongest monocular response, if both eyes are stimulated. Psychophysical data follows the same power law as the neural data, with a similar exponent; binocular contrast sensitivity can be modeled as a gated amplification of the more sensitive eye. These results resemble gated amplification phenomena in multisensory integration, and other non-driving modulatory interactions that affect sensory processing. Models of incomplete summation seem unnecessary for V1 facilitatory neurons or contrast sensitivity. However, binocular combination of clearly visible monocular stimuli follows Schrödinger’s nonlinear magnitude-weighted average. We find that putatively suppressive binocular neurons closely follow Schrödinger’s equation. Similar suppressive multisensory neurons are well documented but seldom studied. Facilitatory binocular neurons and mildly suppressive binocular neurons are likely neural correlates of binocular sensitivity and binocular appearance respectively.