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Homework Statement
I've been asked as a part of some school project to find the Fourier transform, and time evolution of the following initial wavefunctions:
1. ##\Psi(x,0) = Ae^{\frac{-x^2}{2\sigma ^2}}##
2. ##\Psi(x,0) = Be^{\frac{-x^2}{2\sigma ^2}}e^{\frac{ipx}{\hbar}}##
What physical difference does the ##e^{ipx}## term make?
To find the time evolution of 1 and 2, do I follow the following steps?
1. Normalize them
2. Find their Fourier transform
3. Plug it into their inverse Fourier transform ##\int \frac{\tilde{\psi}}{\sqrt{2\pi}} e^{i(kx - \frac{\hbar k^2}{2m} t)}##
I was told to take ##\hbar = 1## and therefore ##p = k##
Assistance is greatly appreciated