Bohmian trajectories for time dependent wave functions

[MarkDPhysics]

I've been studying the 2D time-dependent two-slit diffraction example. I'm trying to understand the units of the time degree of freedom. If I modify the potential to be all zero, then I should just get the free particle Gaussian wave packet in 2D which is solvable analytically. When I do this, it looks like the phase velocity at the center of the Gaussian wave packet is quite a bit slower than the motion of the wave packet's density center, and I think they should be about the same. I'm trying to use qmsolve to simulate Bohmian trajectories and eventually stochastic mechanics trajectories, and so I want to make sure that the Gaussian case looks right as a sanity check. Peter Holland's book "The Quantum Theory of Motion", chapter 4, covers this in some detail. Has anybody thought to try and use qmsolve for calculating Bohmian trajectories yet? It seems like an obvious thing to do.

[MarkDPhysics]

Let me correct what I said above. I meant to say that the Bohmian velocity for the Gaussian wave packet at the center of the packet should move with about the same velocity as the overall wave packet. The phase velocity is different. I'm finding the Bohmian velocity is moving slower than the wave packet, but this might be a units problem. See for example Holland's book, eqn. 4.7.8. I assume that I need to use atomic units for both the time variable and the space coordinates, so that Bohmian Velocity = grad(S), otherwise there can be a unit-dependent factor multiplying the grad term which is hbar/mass in whatever units you have. But when I try and do that the Bohmian trajectories are moving slower than the wave packet center.

[marl0ny]

It may also be possible that the wavelength used in your Gaussian wave packet is not large enough for the grid discretization to resolve. If that is the case perhaps you can try decreasing its initial average momentum. There may also be issues on your end with how you’re numerically integrating the particle’s trajectory.

[MarkDPhysics]

Good suggestions. Thanks.

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On Sat, Jan 27, 2024 at 1:07 PM Mark Lamorena ***@***.***> wrote: It may also be possible that the wavelength used in your Gaussian wave packet is not large enough for the grid discretization to resolve. If that is the case perhaps you can try decreasing its initial average momentum. There may also be issues on your end with how you’re numerically integrating the particle’s trajectory. — Reply to this email directly, view it on GitHub <#30 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/BFGULYKLV74GLKS2SF3L2VTYQVUBTAVCNFSM6AAAAABCM3R5MCVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMYTSMJTGMZTMMJQGE> . You are receiving this because you authored the thread.Message ID: ***@***.***>