# spectrum of an operator

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## 4 matching pages

##### 1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

##### 2: 18.39 Applications in the Physical Sciences

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►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.
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►The spectrum is entirely discrete as in §1.18(v).
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►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 $\pm \mathrm{\infty}$ 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 ${\mathbf{E}}_{n}$

… ►The*spectrum*of such self-adjoint operators consists of their eigenvalues, ${\lambda}_{i},i=1,2,\mathrm{\dots},n$, and all ${\lambda}_{i}\in \mathbb{R}$. …

##### 4: Bibliography S

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An Introduction to the Operations with Series.
2nd edition, Chelsea Publishing Co., New York.
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The Bound State of Weakly Coupled Schrödinger Operators in One and Two Dimensions.
Annals of Physics 97 (2), pp. 279–288.
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Operators with Singular Continuous Spectrum: I. General Operators.
Annals of Mathematics 141 (1), pp. 131–145.
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An Introduction to Classical Electromagnetic Radiation.
Cambridge University Press, Cambridge-New York.
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An Atlas of Functions.
Hemisphere Pub. Corp., Washington.
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