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The first section deals with solving your schrodeinger equation with some harmonic potential of mx^2 or something like that. Their are several methods on how to solve this particular equation which produces a series of formulas.

The Second part used some fourier analysis to describe the motion of the wave packet, which I can understand ... however how they got to the fourier integral and the expression of it all is beyond me.

It seems when I was reading my book on how it arrived to the equation, that either the method they used was too long or they assumed or made up a number of ridiculous expressions to got to the equation; by the time they get to the result I long forgot what they set out to do.

Is this how quantum mechanics is suppose to be, a number of ambiguous assumptions and rules that are made up that you must blindly follow to get to some result that you don't even understand?