Do i have to transplant?

So can i just put my plants in a 3 gallon container since i only want them 3 feet tall and just grow them without changing the pots. Or must i transplant and if so why is it necessary? and is there any scientific evidence backing it up?

Your plant is going to keep "growing" and looking for new nutrients. As soon as it senses that it has no more room to expand and find new nutrients, oxygen, etc, the plant sort of goes into "panic" mode. They can do anything from drop off a few leaves, to die.
The following symptoms may be observed if you allow your plants to become root-bound:
1. Stunted Growth.
2. Stretching.
3. Smaller and slower bud production.
4. Needs watering too often.
5. Easy to burn with low % nutrient solution mixtures.
6. Wilting.
7. Autoflowering.

Now, onto your question. The "rule of thumbs" is "One gallon per foot" but I think thats not enough. I'd never do a soil grow in less then 5 gallon containers. There is a lot of science backing it up; and plenty of easy to follow logic too. I don't wanna grab a ton of links right now, but I promise you, its true. Lol Im sleepy, ill post links to some real resources tomorrow when I get up if you're still feeling shaky.