APL and Quantum Mechanics

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APL and Quantum Mechanics

Postby ray on Tue Sep 27, 2016 12:18 pm

I have come across no references to APL and Quantum Physics.

Has any one here tried using APL in place of Paul Dirac's "bra-ket" notation?

Despite "vectors", "matrices", "functions", "operators", "inner products" and many other terms used in Quantum Mechanics that are very familiar to APLers, I am having a hard time coming to grips with some of the terminology and notation used in Quantum Mechanics. But have found that when expressed in APL notation some become much easier to visualize and/or comprehend.


With the introduction of complex numbers into Dyalog APL, Dirac's "ket"s and "bra"s are now easily represented, and many of the operations (such as "Hermitian conjugate" -the complex conjugate of a transposed matrix) are easily performed (even if not easy to say).

For instance, how could the Dirac notation
<⍺|M|⍺>

be (re)written in APL?
Would it involve trains?

(I am currently struggling with the book "Quantum Physics for Dummies" and Leonard Susskind's book and YouTube course "Quantum Mechanics - The Theoretical Minimum".)

Is anybody else interested in this area?
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Re: APL and Quantum Mechanics

Postby ArrayMac227 on Fri Sep 30, 2016 3:03 pm

Do you have an online reference for this notation?
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Re: APL and Quantum Mechanics

Postby ray on Sun Oct 02, 2016 2:04 am

The Wikipedia reference is as good as any:

https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation

A simple example of a ket and bra:
Given a vector A of complex numbers

Code: Select all
       A←  3j4 0j¯1
┌→───────┐
│3J4 0J¯1│
└~───────┘

  ⍝ ket  |A>  ←→  2 1⍴A     
┌→───┐
↓3J04│
│0J¯1│
└~───┘

   ⍝ bra <A|  ←→  1 2 ⍴+A   
┌→───────┐
↓3J¯4 0J1│
└~───────┘
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Re: APL and Quantum Mechanics

Postby Bob Armstrong on Sun Oct 02, 2016 3:08 pm

A few years ago I "inherited" my niece's Electrodynamics and Quantum texts , both by Griffiths , that they use at Boulder . It seems each generation has some particularly brilliant textbook writer who dominates his market and Griffiths is one .

I was particularly interested in the Electrodynamics because of my interest in understanding , ie : implementing , the essential computations of planetary temperature , that is , the radiant heat transfer supposedly underlying the greenhouse gas effect . See http://cosy.com/#PlanetaryPhysics and particularly my presentation of the most basic calculations for a radiantly heated colored ball , like our Earth , all in K , at the Heartland conference a couple of years ago . http://climateconferences.heartland.org/robert-armstrong-iccc9-panel-18/ . The conclusion is : no spectral effect can explain why the bottoms of atmospheres are hotter than their tops , and the whole paradigm is Bull . I later came to understand it's because gravity is indefensibly left out of the balance -- tho I'll leave those computations until someone is interested in implementing them in 4thCoSy.

In any case , I think Dirac notation sucks . It's one of those notations that seems to get created , like some of Einstein's , and the field gets stuck with it like querty ( tho krazy glue isn't as sticky as querty) .

It would be nice to see these topics expressed in APL . I only got involved in the battle against the global statist anti-science , anti-freedom , anti-life ( on the molecular level ) anti-CO2 fraud because I could implement the equations trivially in K and play with them , and thus understand them . Having that ability to implement such computations always at my fingertips is what has driven my life ever since learning APL and being able to write a definitional Fourier transform in one line to analyze a classic psychophysical experiment was the straw which got me ostracized from grad school after a decade . It's always been the personal Tool of Thought aspect of APL which has motivated me rather than massive number-crunching applications and which eventually drove me to roll my own from the chip up in Forth . See http://cosy.com/y16/CoSy20160915.html for the current status .
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