- #1
silimay
- 25
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Sorry... my message got posted by mistake before I started typing. Here is what I was going to say:
I'm having a problem just understanding something from my quantum book. They're deriving something to do with a wave packet with the Schrodinger equation, and they have the equation of a wave packet at time t = 0:
\psi(x,0) = \int_{- \infty}^{+ \infty} dk A(k) e^{i(kx)
where A(k) = e^{- \alpha (k - k_o)^2 / 2}
They change variables to q' = k - k_o and then they get
\psi(x,0) = e^{i k_o x} e^{- x^2 / {2 \alpha}} \int_{- \infty}^{+ \infty} dq' e^{- \alpha {q'}^2 / 2}
I don't understand how they got that (specifically, the e^{-x^2 / {2 \alpha}} term).
I'm having a problem just understanding something from my quantum book. They're deriving something to do with a wave packet with the Schrodinger equation, and they have the equation of a wave packet at time t = 0:
\psi(x,0) = \int_{- \infty}^{+ \infty} dk A(k) e^{i(kx)
where A(k) = e^{- \alpha (k - k_o)^2 / 2}
They change variables to q' = k - k_o and then they get
\psi(x,0) = e^{i k_o x} e^{- x^2 / {2 \alpha}} \int_{- \infty}^{+ \infty} dq' e^{- \alpha {q'}^2 / 2}
I don't understand how they got that (specifically, the e^{-x^2 / {2 \alpha}} term).
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