Heisenberg and the wave-particle dualism

[parton]

Hi!

I am a bit confused about something Heisenberg said about the wave-particle dualism.
In his book about physics and philosophy he wrote:

"The dualism between the two complementary pictures - waves and particles - is also clearly brought out in the flexibility of the mathematical scheme. The formalism is normally written to resemble Newtonian mechanics, with equations of motion for the co-ordinates and the momenta of the particles. But by a simple transformation it can be rewritten to resemble a wave equation for an ordinary three-dimenslonal matter wave."

Could anyone tell me how these equations and in particular, this "simple transformation" explicitly looks like?

Thanks!

 

[Orodruin]

Are you trying to learn physics from a 60 years old popular text?

 

[jfizzix]

If I had to guess, I would say Heisenberg is referring to the ease that one can switch between different "pictures" in quantum physics.

In the Heisenberg picture, the observables evolve in time, while the quantum state is fixed.
In the Schrödinger picture, the observables are fixed, while the quantum state evolves in time.

When it comes down to computing any probabilities or observable statistics, these two pictures are mathematically identical, though sometimes one picture ends up being easier to use than the other.

For a fuller description, see:
https://en.wikipedia.org/wiki/Heisenberg_picture

 

[PeterDonis]

Moderator's note: thread level changed to "I".

 

[PeterDonis]

Could anyone tell me how these equations and in particular, this "simple transformation" explicitly looks like?

Have you tried looking up "Schrödinger Equation"?

 

[parton]

Are you trying to learn physics from a 60 years old popular text?

No, actually I already studied physics some time ago. But now when I read this text from Heisenberg (which is quite interesting to read even nowadays), I am not sure what he really means at this point.

If I had to guess, I would say Heisenberg is referring to the ease that one can switch between different "pictures" in quantum physics.

But is there really a connection between the different pictures and the wave-particle-dualism? Or is there something else in the mathematical formalism that reflects this dualism?

 

[Demystifier]

"The dualism between the two complementary pictures - waves and particles - is also clearly brought out in the flexibility of the mathematical scheme. The formalism is normally written to resemble Newtonian mechanics, with equations of motion for the co-ordinates and the momenta of the particles. But by a simple transformation it can be rewritten to resemble a wave equation for an ordinary three-dimenslonal matter wave."

Could anyone tell me how these equations and in particular, this "simple transformation" explicitly looks like?

Google Heisenberg picture and Schrödinger picture.
A compact summary is given here: https://en.wikipedia.org/wiki/Schrödinger_picture#Summary_comparison_of_evolution_in_all_pictures

 

[parton]

Ok, now I understand. You are right. Indeed, it is related to the different pictures, I just needed to remember :)
Thank you very much!