Re: [xmds-user] Bessel cylindrical coordinates normalisation

[Mattias J. <mat...@mq...>]

Hi Chris,

I'm not very familiar with the Bessel transform, but after having a quick look at XMDS2's code, here's what I can tell you.

Regarding including the r=0 point: When using the Bessel transform, the position of the grid points are given by the zeroes of the Bessel function (multiplied by a scaling factor).

>From the documentation: http://www.xmds.org/reference_elements.html#the-bessel-and-bessel-neumann-transforms: "The order m of the transform is defined by the order attribute in the <dimension> element, which must be assigned as a non-negative integer. If the order is not specified, it defaults to zero which corresponds to the solution being independent of the angular coordinate θ."

So if you're choosing the default order, it's a Bessel function of the first kind with m=0, which doesn't have a zero at the origin.

Regarding your normalisation issue, I'm afraid I have no idea what the problem is.

Cheers,
Mattias
________________________________
From: Craig Chisholm via xmds-user <xmd...@li...>
Sent: Tuesday, 8 February 2022 9:26 PM
To: xmd...@li... <xmd...@li...>
Subject: [xmds-user] Bessel cylindrical coordinates normalisation

Hello,

I am having trouble with using the Bessel transform in cylindrical coordinates. Specifically, I have two problems:

  1.  I see that the normalisation of the wavefunction is evolving over time in spite of using continuous normalisation.
  2.  I would like to have r = 0 as part of the grid for the output but I haven't found a way to do this.

I'm using xmds2 version 2.2.3 "It came from the deep" (Debian package 2.2.3+dfsg-5) on Ubuntu 18.04 LTS and Linux Mint 19.3 and XMDS2 version 2.2.2 "XMDS2 is a game of two halves" on Ubuntu 16.04 LTS. On all three systems it's the same.

Please let me know if I should be providing additional information or diagnostics.

Thank you,


Craig Chisholm

PhD Student
ICFO - The Institute of Photonic Sciences
Av. Carl Friedrich Gauss, 3
08860 Castelldefels
Barcelona, Spain
Research Group: Ultracold Quantum Gases
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