Correspondence principle in arbitrary coordinates

In summary, the conversation discusses the correspondence principle in theoretical physics and the reason why it only works in cartesian coordinates. The participants are seeking an explanation for this limitation and one person suggests that it may be due to the behavior of quantum systems not always matching that of classical systems in non-Cartesian coordinates.
  • #1
QuantumCosmo
29
0
Hi,
I am currently learning for a test in theoretical physics and in one of my books it was mentioned that there is a reason why the correspondence principle only works in cartesian coordinates. Sadly, they didn't give that reason nor a book or website where one could look it up if interested.
Does anyone here know why it only works in cartesian coordinates?
Thanks in advance,
QuantumCosmo
 
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  • #2
Not really. The correspondence principle says that (Wikipedia) "the behavior of a quantum system reproduces that of a classical system in the limit of large quantum numbers". All I can think of is that in non-Cartesian coordinates the correspondence does not always hold going the other way, and low quantum numbers are sometimes necessary too. For example a classical system that was axially symmetric would have m = 0.
 

FAQ: Correspondence principle in arbitrary coordinates

What is the correspondence principle in arbitrary coordinates?

The correspondence principle in arbitrary coordinates is a fundamental concept in physics that states that in the limit of large quantum numbers, the predictions of classical mechanics should match those of quantum mechanics. In other words, as the quantum numbers become very large, the behavior of the quantum system should resemble that of a classical system.

Why is the correspondence principle important?

The correspondence principle is important because it helps bridge the gap between classical and quantum mechanics. It allows us to understand how classical behavior emerges from the underlying quantum nature of particles. It also provides a useful tool for approximating quantum systems using classical mechanics in certain situations.

How is the correspondence principle applied in arbitrary coordinates?

In arbitrary coordinates, the correspondence principle is applied by transforming the equations of quantum mechanics into the corresponding classical equations in the same coordinate system. This allows us to compare the behavior of the quantum system with its classical counterpart and determine if they are in agreement.

What are the limitations of the correspondence principle in arbitrary coordinates?

While the correspondence principle is a useful tool, it has its limitations. It only applies in the limit of large quantum numbers and breaks down for systems with small quantum numbers. It also does not fully explain all quantum phenomena and there are cases where classical mechanics cannot accurately describe the behavior of a quantum system.

How does the correspondence principle relate to the uncertainty principle?

The correspondence principle and the uncertainty principle are complementary concepts in quantum mechanics. The correspondence principle explains how classical behavior emerges from quantum systems, while the uncertainty principle sets limits on the precision with which certain pairs of physical properties can be known simultaneously. In a way, the correspondence principle can be seen as a macroscopic approximation of the uncertainty principle in the limit of large quantum numbers.

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