I took transistor theory years ago. I remember almost nothing of the formulas, but I do remember the presentation. The engineering professor started with a quantum mechanical model, and he expanded the formula till it filled a chalk board. Then he said, notice that the dominate term is, and circled one of the terms. Then he took and erased everything but that term, and said we'll treat this as equal. He did this three times, with one of the formula expansions taking up 3 chalkboards. In the end, he said
and that is why we treat transistors as a linear amplifier, and it only applies across a certain range. Then the next day we had the lab, and the challenge was to build a 2 transistor amplifier and show that it was linear across the desired range. You get the parts, and get them it all together up on a scope. It was a mess, there were odd side-bands and crazy noise points all through the spectrum, and I spent hours tuning the resistors to lock in the range. Wow, it was eye opening. Yes, one can model transistors as a linear amplifier, but it's good to know that the full model is a huge complicated noisy quantum mechanical problem that would probably take up 20 chalk boards fully expanded.
It's like Box said,
all models are wrong, some are useful The linear model of a transistor has proven very useful, but one needs to always be aware of the boundaries where it doesn't apply--for any model.