polar%20coordinates
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1: 1.5 Calculus of Two or More Variables
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§1.5(ii) Coordinate Systems
… ►Polar Coordinates
… ►Cylindrical Coordinates
… ►Spherical Coordinates
… ►For applications and other coordinate systems see §§12.17, 14.19(i), 14.30(iv), 28.32, 29.18, 30.13, 30.14. …2: 36.13 Kelvin’s Ship-Wave Pattern
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►In a reference frame where the ship is at rest we use polar coordinates
and with in the direction of the velocity of the water relative to the ship.
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3: 18.39 Applications in the Physical Sciences
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►where is a spatial coordinate, the mass of the particle with potential energy , is the reduced Planck’s constant, and a finite or infinite interval.
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►Now use spherical coordinates (1.5.16) with instead of , and assume the potential to be radial.
…By (1.5.17) the first term in (18.39.21), which is the quantum kinetic energy operator , can be written in spherical coordinates
as
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►Derivations of (18.39.42) appear in Bethe and Salpeter (1957, pp. 12–20), and Pauling and Wilson (1985, Chapter V and Appendix VII), where the derivations are based on (18.39.36), and is also the notation of Piela (2014, §4.7), typifying the common use of the associated Coulomb–Laguerre polynomials in theoretical quantum chemistry.
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4: 22.18 Mathematical Applications
5: 36.7 Zeros
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►There are also three sets of zero lines in the plane related by rotation; these are zeros of (36.2.20), whose asymptotic form in polar coordinates
is given by
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6: 36.5 Stokes Sets
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►For , the Stokes set is expressed in terms of scaled coordinates
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36.5.7
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36.5.10
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►With coordinates
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36.5.17
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7: 20 Theta Functions
Chapter 20 Theta Functions
…8: 29.18 Mathematical Applications
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§29.18(i) Sphero-Conal Coordinates
… ►when transformed to sphero-conal coordinates : … ►
29.18.4
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