Please bear with me..
In the above image, we need to substitute p2 from the partial derivative (pay attention to content in red boxes). If we're considering the one dimensional case, we can either take a second derivative or square the equation to obtain p2. However, the result won't be the same when substituted (Obviously, as expression has changed). Since p is a vector here (momentum), we can't square anyway. But if we're only considering x (one-dimension) then it should be okay, right?
I don't understand how we can get to expressions for p2 with these two methods (squaring and second derivative) :(
Am I missing something? What does it mean to square a partial derivative? Please help.