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galactic

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- 1

**A particle of mass**

*m*is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2.*The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at t=0.*I know the process of solving PDE's clear as day, thats not the issue. The problem is that I'm tripping myself out on how to write [itex]\Psi(x,t)[/itex] as a linear combination of its ground state + first excited state.

My hunch is to approach the problem like this :

[itex]\Psi(x,t)[/itex]=c[itex]_{0}[/itex][itex]\Psi_{0}(x,t)[/itex]+c[itex]_{1}[/itex][itex]\Psi_{1}(x,t)[/itex]

where 0 and 1 represent the ground state and first state, respectively

I'm confusing myself on what needs to fill in the equations! Any help would be appreciated.

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