# Heisenberg vs schrodinger picture

1. Jan 29, 2005

### 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 Schrodinger 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)?

2. Jan 29, 2005

### dextercioby

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

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

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

Daniel.

3. Jan 29, 2005

### 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 :grumpy: . 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.

4. Jan 29, 2005

### dextercioby

That's true.

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

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

Daniel.