Early Development of Matrix Mechanics: Frequencies, Intensities & Electrons

[Pollock]

I would like to know more about the early development of matrix mechanics.Heisenberg originally represented the frequencies and the intensities of hydrogen spectral lines as two matrices.How were these observables then transformed into information about position and momentum of the electrons responsible for the sprctral transitions ?.The two matrices did not commute,but as I understand it,the significance of this wasn't realized at first,but what does the product of an frequency matrix and an intensity matrix represent anyway ?.
I do not have access to a scientific library and I probably wouldn't understand the original papers even if I had them,but there must be some easy-ish "stepping stones" into this area without the need for Hermitian operators and Hilbert space.
Will someone help,please!.

 

[tiny-tim]

Max Born and matrix mechanics

I would like to know more about the early development of matrix mechanics.Heisenberg originally represented the frequencies and the intensities of hydrogen spectral lines as two matrices.

No, Heisenberg knew nothing about matrices when he wrote his original paper … Max Born developed the matrix representation of Heisenberg's theory …

see eg http://en.wikipedia.org/wiki/Max_Born#Career" …

In the paper, Heisenberg formulated quantum theory avoiding the concrete but unobservable representations of electron orbits by using parameters such as transition probabilities for quantum jumps, which necessitated using two indexes corresponding to the initial and final states. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices …
…
In 1954, Heisenberg wrote an article … credited Born and Jordan for the final mathematical formulation of matrix mechanics

 

[Pollock]

Yes,I was already aware that Heisenberg didn't use the term matrix until Born recognised what he was doing,but you haven't said anything about how the two indexes relate to the position and momentum of the electron in a particular transition.
I think I need something more authorative than an article in the wikipedia.Can you give a summary of the Born/Jordan/Heisenberg paper ?.

 

[badphysicist]

I like the book Quantum Mechanics in Simple Matrix Form by Thomas F. Jordan. It talks somewhat about the development though it might not be exactly what you're looking for.

 

[Pollock]

Thank you for your response.Yes,I have a copy of Jordan's book;when I first saw the title in the Amazon site,I thought -great,this is just what I'm looking for.But I have to say I was somewhat disappointed with it.In some places it is so simple as to be trivial,while in other places it needs fuller explanations.I guess I need to get to grips with the Born/Heisenberg/Jordan paper of 1925.Any suggestions where I might get a translation of it,or better still,a simplified guide to it ?