Matrix Mechanics and non-linear least squares analogy?

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SUMMARY

The discussion centers on the relationship between non-linear least squares curve fitting and Matrix Mechanics in quantum physics. The author draws parallels between fitting a Gaussian curve using a model matrix and the application of Matrix Mechanics, questioning whether it operates on a "model" matrix akin to density or scatter matrices. Key concepts include the use of eigenstates of the Hamiltonian and the role of the Schrödinger Equation in determining wave functions and their evolution over time. The conversation highlights the importance of understanding eigenvalues and eigenvectors in the context of quantum mechanics.

PREREQUISITES
  • Non-linear least squares curve fitting techniques
  • Matrix Mechanics principles in quantum physics
  • Eigenvalues and eigenvectors in linear algebra
  • Schrödinger Equation and its applications
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  • Explore advanced applications of non-linear least squares in data fitting
  • Study the derivation and implications of the Schrödinger Equation
  • Investigate the role of density operators in quantum mechanics
  • Learn about Hamiltonian operators and their significance in quantum systems
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Quantum physicists, mathematicians, and researchers interested in the mathematical foundations of quantum mechanics and the application of linear algebra in physical systems.

  • #31
Yes,
$$|\phi \rangle = \hat{\vec{p}} |\psi \rangle$$
is a correct notation. Note that these are three vectors, because ##\hat{\vec{p}}## are the three operators for the three components of momentum.
 

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