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Homework Statement
[itex]\Psi(x,t) = \int^{\infty}_{-\infty} C(p)\Psi_{p}(x,t) dp[/itex]
is a solution to the Schroedinger equation for a free particle, where
[itex]\Psi_{p}(x,t) = Ae^{i(px-Ept)/\hbar}[/itex].
For the case [itex]C(p) = e^{-(p-p_{0})^{2}/\sigma}[/itex]
where [itex]\sigma[/itex] is a real constant, compute the wavefunction at time t=0.
Homework Equations
[itex]\int^{\infty}_{-\infty} e^{-αp^{2}+βp} = \sqrt{\frac{\pi}{α}}e^{\frac{β^{2}}{4\alpha}}[/itex]
where α is a positive real constant and β may be complex.
2. The attempt at a solution
This is the first part of one questions on a set of QM problems I've been given. I've made no progress with this part, because I don't know how to integrate the product of an exponential to a real number and an exponential to an imaginary number.