Correspondence principle in arbitrary coordinates

  • Context: Graduate 
  • Thread starter Thread starter QuantumCosmo
  • Start date Start date
  • Tags Tags
    Coordinates Principle
Click For Summary
SUMMARY

The correspondence principle in quantum mechanics states that the behavior of a quantum system approximates that of a classical system as quantum numbers become large. This principle is primarily applicable in Cartesian coordinates due to the mathematical properties that facilitate this transition. In non-Cartesian coordinates, such as cylindrical or spherical systems, the correspondence may not hold consistently, particularly at low quantum numbers, as demonstrated by systems with axial symmetry where m = 0. Understanding these limitations is crucial for theoretical physics applications.

PREREQUISITES
  • Fundamentals of quantum mechanics
  • Classical mechanics principles
  • Coordinate systems in physics
  • Mathematical analysis of limits and asymptotic behavior
NEXT STEPS
  • Study the implications of the correspondence principle in quantum mechanics
  • Explore the mathematical properties of Cartesian versus non-Cartesian coordinates
  • Investigate quantum systems with axial symmetry and their behavior
  • Review literature on quantum-classical correspondence, focusing on specific cases
USEFUL FOR

Theoretical physicists, students preparing for advanced physics examinations, and researchers interested in the foundations of quantum mechanics.

QuantumCosmo
Messages
29
Reaction score
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
 
Physics news on Phys.org
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.
 

Similar threads

High School Uncertainty Principle versus spin alignment
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Theoretical status of the Landauer Principle
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Dot product of two vector operators in unusual coordinates
  • · Replies 14 ·
Replies
14
Views
3K
High School Invariant under rotation: Banal, obvious, or noteworthy?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Electric Field & Interplay between Coordinate Systems | DJ Griffiths
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Are all quantum computers feedforward networks?
  • · Replies 14 ·
Replies
14
Views
3K
Graduate Variation in Schwinger's quantum action principle
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Weyl tensor and coordinate acceleration
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Coordinate Transformation versus Change of Synchrony Convention
  • · Replies 9 ·
Replies
9
Views
1K
Undergrad Why could magnetic monopoles exist?
  • · Replies 12 ·
Replies
12
Views
3K