Equation of motion from matrix

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SUMMARY

The discussion focuses on deriving the equation of motion from a Hamiltonian represented in matrix form. For classical mechanics, the use of Poisson brackets is essential, as outlined in the MIT OpenCourseWare resource. In contrast, for quantum mechanics, it is necessary to decompose the matrix using Dirac bra and ket eigenvectors. This distinction is crucial for correctly applying the appropriate mathematical framework based on the nature of the system.

PREREQUISITES
  • Understanding of Hamiltonian mechanics
  • Familiarity with Poisson brackets
  • Knowledge of quantum mechanics and Dirac notation
  • Proficiency in matrix algebra
NEXT STEPS
  • Study the application of Poisson brackets in classical mechanics
  • Explore Dirac notation and its use in quantum mechanics
  • Review Hamiltonian dynamics in both classical and quantum contexts
  • Investigate matrix decomposition techniques relevant to physical systems
USEFUL FOR

Physicists, mathematicians, and students studying classical and quantum mechanics, particularly those interested in the mathematical foundations of motion equations.

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How can I find the equation of motion of a system with the Hamiltonian in matrix form?
 
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I assume given the nature of the question you are adept with the mathematics but I am unsure if you are dealing with a quantum or classical mechanics problem. If it is classical you need to use a Poisson bracket see http://ocw.mit.edu/ans7870/18/18.013a/textbook/chapter16/section03.html
If it is a quantum problem then decompose the matrix in Dirac bra and ket eigenvectors
 
Thank you.
 

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