# schrodinger eq time propagation with dissipation using split step operator

I am looking in ways to include energy dissipation while propagating a coherent wavepacket in a 1d TDSE. for example I use the split step method: exp[Δt(D+V)]≈exp[ΔtV/2]exp[ΔtD]exp[ΔtV/2], and subtract some epsilon value from the kinetic energy term every step. What other ways can I dissipate energy from the system so it'll relax to its equilibrium position?

• Do you want the groundstate? For this, you can use imaginary time-propagation. May 14, 2022 at 7:43
• I want to eventually get to the ground state, but I mostly to model the time it takes to get there by tuning the way the system couples to a "bath". So I want to add a "bath" term with some degree of control, in a way that is physically justified. May 15, 2022 at 18:57
• Ok, but then you need to define the bath-interaction physically from the first (e.g. by a Lindbladt equation or something like that). It makes no sense to adjust something numerically and trying to get some meaningful results. May 15, 2022 at 19:24
• so I guess that is my question. How to define that in order to be able to solve it via split step. maybe split step is not the right method? Is the Lindbladt eq something that I can add to the propagation? May 16, 2022 at 17:50
• That"s definitely the wrong direction. First the equation, then the solution method. I'd suggest you read up tje literature on how to include dissipative boundaries. Yet, you'll be quickly in some kind of density matrix or Green's function formalism, where split-step might be a tool but not the main solution method. May 16, 2022 at 22:18