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nortonian
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Am I right in thinking that the Heisenberg matrix interpretation describes emission, while the Schroedinger interpretation does not?
dextercioby said:Well, essentially they're one and the same thing: either wave mechanics or matrix mechanics, it doens't matter. Either the Schroedinger picture (evolution of the states) or Heisenberg picture (evolution of the observables), or interaction picture (evolution of both categories), it doesn't really matter.
The only reason we choose though one of them over the other is the easiness we seek for making the calculations.
.nortonian said:As I said in my previous message the two pictures may be mathematically equivalent, but the H picture uses discrete time and the S picture uses continuous time. Matrix mechanics consists of compilations of discrete transitions (photons) in arrays while the S wave equation describes a standing wave, not an emitted photon. [...]
dextercioby said:.
With green I've marked the right part of the quoted section of your post.
nnnm4 said:Well nortonian you seem to have your ideas about the Heisenberg picture wrong.
nortonian said:Am I right in thinking that the Heisenberg matrix interpretation describes emission, while the Schroedinger interpretation does not?
nnnm4 said:Anyway, the way I see it there is no distinction between whether H or S is more real. Neither picture, as you pointed out, makes any difference when one considers only observable quantities, i.e. the matrix elements of the operator under question.
The Heisenberg picture is a formulation of quantum mechanics that describes the evolution of a system by keeping the operators fixed and allowing the state vectors to change over time. In this picture, the emission of a particle is described as a change in the state vector, while the operators remain fixed. This allows for a more intuitive understanding of the emission process.
In the Schroedinger picture, both the operators and state vectors evolve over time. This means that the emission process is described as a change in both the state vector and the operators, making it less intuitive to understand compared to the Heisenberg picture.
The Heisenberg picture is preferred for describing emission because it provides a more intuitive understanding of the process. It also allows for a more direct comparison to classical mechanics, making it easier to apply to real-world systems.
Yes, the Heisenberg picture can be applied to all quantum systems. It is a valid formulation of quantum mechanics and is often used in combination with other formulations, such as the Schroedinger picture, to provide a more complete understanding of a system.
One limitation of the Heisenberg picture is that it does not easily allow for the inclusion of external forces or interactions. This can make it difficult to describe emission in systems with complex external influences. Additionally, the Heisenberg picture can become mathematically cumbersome for systems with a large number of particles.