- #1
maverick280857
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Hello.
I'm teaching myself quantum mechanics. I want to understand the meaning of the following integral representation:
[tex]q^{-\frac{1}{2}} = \kappa \int_{-\infty}^{\infty}\frac{dt}{\sqrt{t}}exp(itq)[/tex]
where [itex]q[/itex] is the quantum mechanical position operator. I know that this is a Fourier Integral, but I want to understand it in a deeper way. I don't know much about operators in such integrals, so I also want to know how to evaluate the right hand side...I'm using the book by Atkinson and Hounkonnou and this is from a problem which asks to prove that
[tex]\left[q^{-\frac{1}{2}},p\right] = -\frac{1}{2}i\hbar q^{-\frac{3}{2}}[/tex]
What is the significance of the integral and of the negative powers?
Thanks.
I'm teaching myself quantum mechanics. I want to understand the meaning of the following integral representation:
[tex]q^{-\frac{1}{2}} = \kappa \int_{-\infty}^{\infty}\frac{dt}{\sqrt{t}}exp(itq)[/tex]
where [itex]q[/itex] is the quantum mechanical position operator. I know that this is a Fourier Integral, but I want to understand it in a deeper way. I don't know much about operators in such integrals, so I also want to know how to evaluate the right hand side...I'm using the book by Atkinson and Hounkonnou and this is from a problem which asks to prove that
[tex]\left[q^{-\frac{1}{2}},p\right] = -\frac{1}{2}i\hbar q^{-\frac{3}{2}}[/tex]
What is the significance of the integral and of the negative powers?
Thanks.
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