versions of QM

[abskebabs]

Hi everybody. I know that there were 3 versions of QM developed in the 1920s, Schrodinger's, Heisenberg's and Dirac's? I am under the impression that Dirac's is supposed to be the most mathematically elegant and shows the equivalance of the other 2, is this correct? Also what do you think are the main diferences between them and which do you personally prefer?

 

Also as a first year student I have only been introduced to Schrodinger's version in my lecture course. Is it generally perceived to be the easiest version to understand or use?

[Tom Mattson]

Hi everybody. I know that there were 3 versions of QM developed in the 1920s, Schrodinger's, Heisenberg's and Dirac's? I am under the impression that Dirac's is supposed to be the most mathematically elegant and shows the equivalance of the other 2, is this correct?

 

Not unless Dirac has some other version of QM of which I am not aware. Dirac's quantum mechanics is relativistic and specifically it describes spin-1/2 particles.

 

And actually, you've left out Bohm's quantum mechanics. From what I've read it describes nonrelativistic quantum phenomena just as well as Schrodinger's and Heisenberg's.

 

Also what do you think are the main diferences between them and which do you personally prefer?

 

For nonrelativistic applications I've only ever used Schrodinger's QM, so Heisenberg and Bohm are off the list for me. For relativistic applications we don't get to choose between Dirac and the various nonrelativistic applications. Rather, we choose between quantum mechanics and quantum field theory. I've only ever used relativistic QM when required to by a professor in a homework problem. When doing particle physics, I apply QFT instead.

 

Also as a first year student I have only been introduced to Schrodinger's version in my lecture course. Is it generally perceived to be the easiest version to understand or use?

 

I haven't studied the other nonrelativistic versions of QM in any detail, so dunno.

[abskebabs]

Not unless Dirac has some other version of QM of which I am not aware.

He did develop his own "nonrelativistic" version of QM, and later showed that Heisenberg's and Schrodinger's were special cases of his own formulation. (I wish I was as good at QM as I am at knowing things about its history!) This was done in 1925 and 1926, before his work on QED.

 

Also I wasn't sure if anyone used Bohmian mechanics, so I kind of forgot about it.

[Tom Mattson]

He did develop his own "nonrelativistic" version of QM, and later showed that Heisenberg's and Schrodinger's were special cases of his own formulation. (I wish I was as good at QM as I am at knowing things about its history!)

 

Are you talking about breaking up the time dependence of operators and state vectors according to Dirac's so-called "interaction pitcure"?

[ajb]

The Schrodinger's and Heisenberg's formulations of quantum mechanics (with finite degrees of freedom) are equivalent. This is the so called Stone-von Neumann theorem. Both pictures are in fact equivalent representations of the canonical commutation relations (CCR).

 

What Dirac did was construct a hybrid of these two picture suitable for discussing scattering. This is the so called Dirac or Interaction picture.

 

First point, the Stone-von Neumann theory does not apply when we have infinite number of degrees of freedom and so does not extend to quantum field theory.

 

Second point, Hagg showed that in relativistic quantum field theory, the interaction picture is not well defined. However, it does seem to work!

 

Also, the standard formulation of quantum field theory is based on the Heisenberg picture. You can construct a Schrodinger picture, but as I said I don't think it is obvious that these two formulations are the same. You then use the interaction picture to construct scattering states and calculate S-matricies, scattering amplitudes etc.

 

All these ideas can be found on google if you care to search.