(Note: this is the new version of the spectrograph with less user control, here is a link to the original version

index.html?old=true)


The only functional difference between the versions is that the old version shows more forbidden transitions when the 'visible colors' button is pressed. If 'old=true' is replaced by 'allowForbidden=true' then all forbidden transitions are shown (including even-even and odd-odd transitions such as are seen in the Northern lights).

This javascript here makes the visible colours of all atoms and monatomic ions using the wave equation. You'll have to zoom in with the arrow keys to see the fine structure. For the old version change the url to end /index.html?old=true. Also any javascript code appended to the url will be executed. This version is meant to be more user friendly -- the checkboxes are un-checked and checked automatically (if you want to control them, use the old version), and also in both versions we've fixed the fact that assinging term symbols to levels and permuting levels don't commute. The easiest way to use it is to type in the number of electrons in the upper left box, then press 'next config' just once (or press enter), and when it is finished, you can press it more times if you want more levels. The arrow keys are for looking more closely at the spectrum, and the button 'show colors' shows which difference corresponds to which spectral line. You should enable popups when they try to appear (these are from NIST to compare with what is found in nature).

Here is a video showing the javascript react while the perturbation coefficient, which multiplies the electrostatic multipole series, changes for Beryllium changing from 0 to 1; the green are actual which get permuted at the end fullscreen.html?file=quantumvideo.mp4. If you check 'use stored coef' it will use a stored number for this perturbation coefficient called pmult, usually 1 or 1.5. A number called emult which is larger multiplies the proton charge (see next paragraph) and the parameter that is changed in the video affecting proportions can be considered as pmult/emult, still a number less than 1.

The coarse correction allows an attempt to correct for the problems the perturbation causes for the sums of reciprocal squares, by artificially increasing the proton charge by a multiple called emult, but only in how it affects levels with differing reciprocal sums of squares (not affecting any spectral frequency which was resolved into a difference if the two electron configurations are the same or even have the same reciprocal sum of squares). But now it also is allowed to affect the fine structure. Once 'next config' stops flashing, the value of emult will be such that if the levels are ordered lexicographically giving the reciprocal sum of squares effect precedence, then the second successive differences within each subsequence where the set of l quantum numbers is constant, is minimized in the least squares sense.

The 'visible colors' button shows details about visible spectral lines, but the display will likely be misleading if care is not taken. To make functions in the webworker available in a browser's developer console, type "loadWorkerAsScript()" and this also loads things like a polynomial algebra script. Many of the functions are intuitively named, so casimirL("1s22p3") is the rotational casimir of the configuration 1s22p3, and times(A,B) is the product of matrices A,B. As a message in the developer's console explains, in order to access all the functions in the webworker you'll want to start by typing "loadWorkerAsScript()."

Examples using the older version:

Here are the electromagnetic equations making the red and green Northern Lights index.html?allowForbidden=true&autocorrect.checked=false&panLeft=160&scaleWidth=4&panLeftSpeed=-.002&scaleWidthSpeed=.15&dofine.checked=true&nextt(8) They represent transitions between even functions.

Here is the green Magnesium star triplet, and press 'next config' a few times after the calculation is definitely done, to see the yellow one. index.html?panLeft=160&scaleWidth=4&panLeftSpeed=-.002&scaleWidthSpeed=.15&emult=4.5&autocorrect.checked=false&usepmults.checked=false&dofine.checked=true&finecorrect.checked=false&nextt2(12)&nextt2(12)&nextt2(12). Both are reversed because the p orbital is more than half full.

Here is the familiar bright yellow Sodium doublet index.html?autocorrect.checked=false&dofine.checked=true&nextt2(11)&nextt2(11)&panLeft=280&scaleWidth=20&panLeftSpeed=-3&scaleWidthSpeed=1.

And the Carbon spectrum, perhaps reminiscent of fire, index.html?panLeft=280&scaleWidth=20&panLeftSpeed=1&scaleWidthSpeed=.1&nextt2(6)&nextt2(6)&nextt2(6)&nextt2(6)&nextt2(6)&nextt2(6)&nextt2(6)&nextt2(6)&nextt2(6)&nextt2(6).

The arrow keys are for looking closer, and 'compare external' compares with what is actually found in nature

Details of the calculation are in 'view source' or in even more detail in chemistry.pdf

Also here is a link to other mathematical papers