Working in the Heisenberg picture and comparing with Schrödinger

[RedX]

How does one work in the Heisenberg picture? Can you dequantize and solve the classical Hamilton's equations and somehow requantize this classical solution for the time evolution of the position and momentum operators (and more importantly the eigenvectors)? How would one go about doing that, and which is more useful, the Schrödinger picture or the Heisenberg picture or the Dirac/interaction/intermediate picture (the latter is where your frame rotates at the rate of the time-independent part of the Hamiltonian)?

 

[dextercioby]

How does one work in the Heisenberg picture? Can you dequantize

What do you mean by "dequantize"??The quantization postulate goes one way only.
Are u referring to Heisenberg & Schroedinger pictures in classical dynamics...??U needn't QM to do that...

and solve the classical Hamilton's equations

No,u do not solve the classical Hamiltonian equations for purpose involving the word "quantum"...

and which is more useful, the Schrödinger picture or the Heisenberg picture or the Dirac/interaction/intermediate picture (the latter is where your frame rotates at the rate of the time-independent part of the Hamiltonian)?

Depends on the situation.They're all EQUIVALENT and useful in the same proportion...

Daniel.

 

[RedX]

It's just that my textbook makes a big fuss about the similarity of Heisenberg's picture to the classical Hamilton's equations, showing that the quantum operators obey the same differential equations as the variables in the classical picture. I was just thinking that you could replace the quantum Hamiltonian with the corresponding classical Hamiltonian (dequantize - I guess I'm inventing words), solve the classical equations for momentum and position variables, and somehow requantize these variablesto get the position and momentum operator as a function of time (hence almost all other variables). Guess I was hopeful that quantum mechanics would be easy . One wonders why the author even bothers pointing out the similarity between classical Hamilton's equations and Heisenberg's picture when you can't use that similarity to your advantage.

 

[dextercioby]

It's just that my textbook makes a big fuss about the similarity of Heisenberg's picture to the classical Hamilton's equations, showing that the quantum operators obey the same differential equations as the variables in the classical picture.

That's true.

I was just thinking that you could replace the quantum Hamiltonian with the corresponding classical Hamiltonian (dequantize - I guess I'm inventing words), solve the classical equations for momentum and position variables, and somehow requantize these variablesto get the position and momentum operator as a function of time (hence almost all other variables). Guess I was hopeful that quantum mechanics would be easy .

Nope,it doesn't work that way.It never will.

One wonders why the author even bothers pointing out the similarity between classical Hamilton's equations and Heisenberg's picture when you can't use that similarity to your advantage.

U can,just as long as u decide to do everything in the Heisenberg picture.Why would you need analogies?

Daniel.