Last night in physics, we were diving further and further into Quantum Mechanics, and my professor gave us a simple derivation of Heisenberg's Uncertainty Principle. However, there is something I don't get. Maybe you guys can help me out. I get all the stuff at the beginning, but its pretty much the last bit where I'm lost...

Due to Taylor Approximations, for small values of

Thus,

From deBroiglie's Equation, we discover that .

Therefore, .

Using the idea that , We can see that .

Thus,

I understand numerically that , but why is it that we say in the Uncertainty Principle that ???

I'd appreciate any input.

--Chris