Schr�dinger Operators
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1—10 of 86 matching pages
1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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Bounded and Unbounded Linear Operators
… ► … ► … ►Self-Adjoint Operators
… ►Spectrum of an Operator
…2: 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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Asymptotische Entwicklungen der Jacobischen Polynome.
Schr. der König. Gelehr. Gesell. Naturwiss. Kl. 10, pp. 33–112.
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3: 25.17 Physical Applications
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►This relates to a suggestion of Hilbert and Pólya that the zeros are eigenvalues of some operator, and the Riemann hypothesis is true if that operator is Hermitian.
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4: 18.42 Software
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►Also included is a website (CAOP) operated by a university department.
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5: 26.19 Mathematical Applications
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►These have applications in operations research, probability theory, and statistics.
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6: Brian R. Judd
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►Judd’s books include Operator Techniques in Atomic Spectroscopy, published by McGraw-Hill in 1963 and reprinted by Princeton University Press in 1998, Second
Quantization and Atomic Spectroscopy, published by Johns Hopkins in 1967, Topics in Atomic and Nuclear Theory (with J.
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7: 13.27 Mathematical Applications
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►Vilenkin (1968, Chapter 8) constructs irreducible representations of this group, in which the diagonal matrices correspond to operators of multiplication by an exponential function.
The other group elements correspond to integral operators whose kernels can be expressed in terms of Whittaker functions.
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8: 18.38 Mathematical Applications
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►A further operator, the so-called Casimir operator
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Dunkl Type Operators and Nonsymmetric Orthogonal Polynomials
►The Dunkl operator, introduced by Dunkl (1989), is an operator associated with reflection groups or root systems which has terms involving first order partial derivatives and reflection terms. … ►In the one-variable case the Dunkl operator eigenvalue equation … …9: 26.22 Software
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►Also included are websites operated by university departments and consortia, research institutions, and peer-reviewed journals.
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10: 34.9 Graphical Method
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►The graphical method establishes a one-to-one correspondence between an analytic expression and a diagram by assigning a graphical symbol to each function and operation of the analytic expression.
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