1.) In Quantum, how are related to each other?

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I was able to do this.

We know the following: . Hence, we're able to find .

2.) Describe the physical meaning of

which is for any wave function.

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The book describes this one as being a Fourier transform and inverting the fourier integral.

Does this move position in momentum?

(On a side note, why don't physics people place the dk, dx etc AFTER the integral!).

3.) Describe the physical meaning of . Why are the uncertainties in and intrinsic rather than being a type of measurement errors.

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Well, I don't understand the intrinsic part. The first part I took straight from my book:

The product of the position and momentum uncertainties and , respectively, of a quantum object is greater than or equal to Planck's constant

Not sure what the second part is asking.

4.) Using (that is the uncertainty relation), determine (estimating) the minimum amount of energy of a particle with mass and with potential energy , where is a pos. constant.

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Not sure.