What {R,G,B} values would represent a 445nm monochrome lightsource color on a computer monitor? Is it possible to answer my question definitely (assuming the monitor is perfect)? What would be the formula for calculating RGB values for a visible monochrome light with given wavelength?
 A: You can use http://rohanhill.com/tools/WaveToRGB/index.asp to convert a wavelength to rgb.
If your interest lies more in what the formula actually is, this would illustrate it

(source: sfasu.edu)
As you see there's not really an exact formula - they use the approximation in that image.
A: There is no way to display a monochromatic light on a RGB monitor: RGB-value is a mixture of three light sources, it cannot be monochromatic by definition even if R, G and B components are monochromatic themselves.
Look at the famous CIE 1931 chromaticity diagram that shows the space of all colors we can see compared to a gamut of a typical monitor. Monochromatic light is the boundary of the color space and the tool in Bruno's answer calculates the closest color within the triangle of RGB values. You can see that for 455 nm this approximation is quite close, whereas green light (like 510 nm) is really far away from what RGB monitor can display.

Edit: as MSalters pointed out, the distance on the CIE 1931 diagram should not be interpreted as difference of two colors as the diagram strongly exaggerates green tones. Other color spaces have been designed where the distance on of two points corresponds to perceived color difference. One of them is CIELUV (L* u* v*) and in this space it doesn't look that green colors are displayed worse than reds or blues.
 
A: Humans have three kinds of cones, which are photoreceptor cells, for color vision in our retina. They can be characterized by their spectral sensitivity, which gives a relative response intensity as a function of wavelength, and which is approximately the same for each individual. The following image gives an average shape for each cone type:

The response to light of a given spectral distribution is fully determined by the triple of values obtained by integrating the product of the spectral distribution with the cone response. If you do this for the spectrum of monochromatic light of 445 nm wavelength, which is a multiple of a delta function, you get a triple $(s,m,l)$, where $s$ will be much larger than the other two (in this case). 
If you do the same for the three kinds of dots your screen is built up of, you get three values for each of them as well. By linear algebra you get a unique linear combination that should reproduce your monochromatic source for as far as human perception is concerned. However, you may very well get negative coefficients. In this case the value is outside the gamut of the monitor.
Finally, the values you have to send to the monitor are not directly these coefficients. From your input to the light intensities there are all kinds of transformations involved. In the best of cases you can specify the values in some standardized colour space, like Lab, XYZ or sRGB. Transformation between these color spaces and the space of cone responses of the average observer is standardised (though not uniquely), see e.g. wikipedia.
A: Well the R and G values would both be zero, and you would have to have a 445nm dominant wavelength blue phosphor or back light source (LED).
Well you can't find that on your computer monitor, as the blue LEDs are more like 460-470 nm.
So there is no solution.
