I Matrix Mechanics and non-linear least squares analogy?

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The discussion explores the analogy between non-linear least squares curve fitting and Matrix Mechanics in quantum physics. It highlights the use of a "model" matrix combined with observed data to find solutions through linear algebra, paralleling how Matrix Mechanics fits observed results to a model matrix. Participants clarify that eigenstates of the Hamiltonian are determined by the system's characteristics, and the Schrödinger Equation is essential for predicting how a system evolves over time. The conversation emphasizes that allowed quantum states can be expressed as linear combinations of eigenfunctions, and the Hamiltonian operator plays a crucial role in this process. Overall, the dialogue seeks to deepen the understanding of how Matrix Mechanics operates within quantum mechanics.
  • #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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