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## Homework Statement

I want to plot a graph of the survival probability of the initial state ψ = e

^{-|x|}for a free particle. Hopefully this will enable me to plot some more difficult examples like the inverted oscillator etc for a project but I'm struggling fundamentally with the free particle.

## Homework Equations

## The Attempt at a Solution

I have tried simple things like trying to calculate the probability using the usual integral over all space but that didn't work. I think I need to use something more complex like a propagator perhaps but my knowledge is very limited. Do I need to confine my wavefunction so it can be normalised? how do I find the time dependence for this initial state?

Any help on how to approach this would be great! I'm ultimately trying to reproduce a graph in mathematica that originated from a paper on tunnelling out of a time dependent well but I am a rookie in this field and I'm trying to teach myself the physics as I go along.