discrete analog
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3 matching pages ♦
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3 matching pages
1: 20.11 Generalizations and Analogs
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►It is a discrete analog of theta functions.
If both are positive, then allows inversion of its arguments as a modular transformation (compare (23.15.3) and (23.15.4)):
…This is the discrete analog of the Poisson identity (§1.8(iv)).
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2: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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► The analogous orthonormality is
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►The analogs of (1.18.49)–(1.18.52) may be written in a similar fashion each now including contributions from both the discrete and continuous parts of the spectrum, as in (1.18.65).
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3: 18.39 Applications in the Physical Sciences
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►However, in the remainder of this section will will assume that the spectrum is discrete, and that the eigenfunctions of form a discrete, normed, and complete basis for a Hilbert space.
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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).
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►Analogous to (18.39.7) the 3D Schrödinger operator is
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►Analogous to (18.39.8) the 3D time-independent Schrödinger equation with potential is
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