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Continuous spectrum (functional analysis)

Ciro Santilli (@cirosantilli, 37) ... Algebra Linear algebra Matrix Eigenvalues and eigenvectors Eigenvalue Spectrum (functional analysis)
Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own version
Unlike the simple case of a matrix, in infinite dimensional vector spaces, the spectrum may be continuous.
The quintessential example of that is the spectrum of the position operator in quantum mechanics, in which any real number is a possible eigenvalue, since the particle may be found in any position. The associated eigenvectors are the corresponding Dirac delta functions.

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  1. Spectrum (functional analysis)
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  • Position representation
  • Solving the Schrodinger equation with the time-independent Schrödinger equation
  • Time-independent Schrödinger equation for a free one dimensional particle

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