1. The problem statement, all variables and given/known data 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. 2. Relevant equations 3. 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.