Can you use a simple lightbulb (halogen, or even the simplest) as a grow light? All biology textbooks indicate that plants use the visible part of the electromagnetic spectrum, which the light of a simple lightbulb is. Plants for photosynthesis use the blue-violet and red parts of the spectrum mostly, and the green is being reflected, so that's why plants seem green. I've noticed that the special grow lights only use the needed parts of the spectrum (blue-violet and red), but why can't you use a simple light that is white (so it's consisted of all the colors)? For example an experiment when you want to find out how much oxygen a water plant produces can be done with a simple lamp.
So?

You can use whatever kind of light source you choose to, a candle or a flash light will work too. But why would you choose not to use a candle or flashlight? Because the candle would die out quickly and give off to much heat when brought close enough to provide usable light. The flashlight would provide better light and allow to be closer/more useable light but would need new batteries daily. Both options would work but would be terribly inefficient.

The answer to your question is there are more efficient options to supply the tree with light then with a halogen or standard light source. The problem with halogen or standard light sources is the PAR (photosynthetically active radiation) to heat ratio renders this type inefficient as a plant light source. Some choose to use lumens per watt as a unit of measure as well. Spectrum, as you mention above is also important, and you are correct blue and red tend to be the usable spectrum. Most of other wavelengths are simply not used, thus not required.

Florescent, LED and HID light sources provide for much better output to heat ratios, better PAR or Lumen per watt efficiency and correct kelvin or spectrum ratings for plants.

With light sources its all about efficiency.

You're right heat is not always bad, it can be a a good thing during cold months. But what about at night, when the light is off, it might get too cold? The halogen you show has a low kelvin rating(around 3,000k), this light will not provide the tree with the proper wavelength, or enough PAR(which will require even more light sources) and generate heat. Why not buy a heater for heat and a compact florescent at 6500k (or even better a Metal Halide) for the tree? this way you have the heat you need for day and night, and the correct light source for the tree, everyone's happy. and if you want burn a candle for an extra boost

Is this what you are talking about?

Because this would actually be even better for me.
But how much watts?

That will be better then the halogen. Try and get a them in higher kelvin ratings, 5,500k-6,500k, they look more blue then red, the red(2,000k) are not as good. you will probably need a few to supply the tree with enough light.

This is the tree I'd like to revive:


As you can see it has little leaves now, wouldn't one light be enough?

And how exactly do I do that? Do I just light it where it stands on a windowsill, or do I put it in a box, and cover the walls with foil to reflect the light?

What about 85W ~5500K-6500K?

As long as temps are good a windowsill would probably be best. I would give it probably 2 of those 85w lights for about 10-12 hours.

Well apparently they don't have 85W bulbs here, the most powerful were 60W in the store, but they were only 2700K

How many lumen citrus require?
AND: do I only grow them under lights all the time? Or do I stand them in the daylight on the windowsill, and then put them under lights? I won't be using the lights on the windowsill, because I live in an apartment, so everyone outside would see the bright bright lights, which I don't want.

Really depends on size, I would guess your tree would do fine with 2 24w 6,500k bulbs. Supplement the natural sunlight, add an hour before sun rises and an hour after sun sets or less if it bothers your neighbors. Or if you decide, move it to away from the window and only supply it with artificial light.

Well I'm getting 2 85W 5500K bulbs, is that too much?

Higher strength light = must have warm roots.

IMO 2 x 85W bulbs = 25-30C roots = 2-3 sets of fairly lights/heat mat

I'm going to stand the box with all the equipment and the plant inside right next to a radiator.