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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