Timeline for How to Perform Fourier Transform on a Quantum State of Spin-1/2 Particle?

9 events

when toggle format	what		by	license	comment
Jun 13 at 22:18	vote	accept	bougab
May 11 at 12:45	comment	added	Níckolas Alves		yes, you apply the Fourier transform only to the position part. I'm just checking really fast, so I might be missing something, but your expression seems correct
May 11 at 7:41	history	edited	Qmechanic♦	CC BY-SA 4.0	edited title
May 11 at 6:13	history	edited	Qmechanic♦		edited tags
May 11 at 4:54	answer	added	flippiefanus		timeline score: 0
May 11 at 2:04	comment	added	bougab		To clarify: when performing the Fourier transform on $\|\psi(0)\rangle$, each component (position and spin) is treated independently, correct? Does this mean I apply the Fourier transform only to the position part and keep the spin part unchanged? Can you confirm if my calculation below is correct? $ \langle p \| \psi(0) \rangle = \frac{1}{(\pi\sigma^2)^{1/4}} (\alpha \|+\rangle + \beta \|-\rangle) \int_{-\infty}^{\infty} dx \exp \left[ \frac{-x^2}{4\sigma^2} \right] \frac{e^{-ipx/\hbar}}{\sqrt{2\pi\hbar}} $
May 11 at 1:51	comment	added	Níckolas Alves		Quick answer: you treat each component independently. You can just pull the tensor product out of the integral and make the change of basis for the continuous variable
S May 11 at 1:42	review	First questions
May 11 at 6:02
S May 11 at 1:42	history	asked	bougab	CC BY-SA 4.0