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spectrum of an operator


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1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
Spectrum of an Operator
2: 18.39 Applications in the Physical Sciences
Also presented are the analytic solutions for the L 2 , bound state, eigenfunctions and eigenvalues of the Morse oscillator which also has analytically known non-normalizable continuum eigenfunctions, thus providing an example of a mixed spectrum. … The spectrum is entirely discrete as in §1.18(v). … The spectrum is entirely discrete as in §1.18(v). An important, and perhaps unexpected, feature of the EOP’s is now pointed out by noting that for 1D Schrödinger operators, or equivalent Sturm-Liouville ODEs, having discrete spectra with L 2 eigenfunctions vanishing at the end points, in this case ± see Simon (2005c, Theorem 3.3, p. 35), such eigenfunctions satisfy the Sturm oscillation theorem. … The radial operator (18.39.28) …
3: 1.3 Determinants, Linear Operators, and Spectral Expansions
§1.3 Determinants, Linear Operators, and Spectral Expansions
§1.3(iv) Matrices as Linear Operators
Linear Operators in Finite Dimensional Vector Spaces
Self-Adjoint Operators on 𝐄 n
The spectrum of such self-adjoint operators consists of their eigenvalues, λ i , i = 1 , 2 , , n , and all λ i . …
4: Bibliography S
  • I. J. Schwatt (1962) An Introduction to the Operations with Series. 2nd edition, Chelsea Publishing Co., New York.
  • B. Simon (1976) The Bound State of Weakly Coupled Schrödinger Operators in One and Two Dimensions. Annals of Physics 97 (2), pp. 279–288.
  • B. Simon (1995) Operators with Singular Continuous Spectrum: I. General Operators. Annals of Mathematics 141 (1), pp. 131–145.
  • G. S. Smith (1997) An Introduction to Classical Electromagnetic Radiation. Cambridge University Press, Cambridge-New York.
  • J. Spanier and K. B. Oldham (1987) An Atlas of Functions. Hemisphere Pub. Corp., Washington.