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 May 3 awarded Popular Question Feb 23 awarded Teacher Feb 23 answered Reciprocal lattice and phonon Jan 18 accepted Dynamics of a Rocket Jan 18 awarded Scholar Jan 18 accepted Simulating the evolution of a wavepacket through a crystal lattice Dec 31 comment Simulating the evolution of a wavepacket through a crystal lattice @hwlau Ashcroft & Mermin has a chapter on semiclassical techniques. However, the equations presented deal with the evolution of a wavepacket under external fields, which is not exactly my problem. Perhaps it is possible to deal with varying $w_n$ as a defect using perturbation theory? A small bounty would be appreciated. Thanks in advance. Dec 31 comment Simulating the evolution of a wavepacket through a crystal lattice @hwlau I'm simulating lattices with the number of sites of order $10^3$. A preparing a Hilbert space of order $O(2^n)$ is still too large. Dec 30 awarded Supporter Dec 30 revised Dynamics of a Rocket added 42 characters in body Dec 30 comment Dynamics of a Rocket Thanks for bringing this up; I forgot to mention that we will be incorporating gravitational force into the differential equation. I will edit my original post to address this change. Regarding the parabolic reference, what I meant is: what if the rocket needs to turn slightly? How do we model the rocket's turning? Or is it ideal for it to travel in a straight line? Dec 30 comment Dynamics of a Rocket Ah, then T must be a function of atmospheric pressure (i.e. a dependent on distance from the Earth then). But rate of fuel consumption will still be constant, right? This is in response to hwlau's saying that T should not be constant -- don't know where that comment went. Dec 30 asked Dynamics of a Rocket Dec 30 comment Simulating the evolution of a wavepacket through a crystal lattice @hwlau I'm unsure how to employ the semiclassical approximation to model the dynamics of this system. Do you have any suggestions or any literature you could point me towards? Thanks. Dec 24 awarded Editor Dec 24 comment Simulating the evolution of a wavepacket through a crystal lattice At the end of the day, I would like to numerically time-step through some differential equation. The question is which differential equation do I solve! Dec 24 revised Simulating the evolution of a wavepacket through a crystal lattice added 9 characters in body Dec 24 comment Simulating the evolution of a wavepacket through a crystal lattice I am more interested in the physical techniques that can be used to simplify the problem and hence, make it computationally viable. As we know, quantum mechanical simulations on classical computers are often intractable as the computational steps required increase exponentially with the degrees of freedom in the system. Dec 24 revised Simulating the evolution of a wavepacket through a crystal lattice edited tags Dec 24 asked Simulating the evolution of a wavepacket through a crystal lattice