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Date: 18-7-2018
1057
Date: 18-7-2018
962
Date: 13-7-2018
1031
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In parabolic cylindrical coordinates, the scale factors are , and the separation functions are , giving Stäckel determinant of . the Helmholtz differential equation is
(1)
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attempt separation of variables by writing
(2)
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then the Helmholtz differential equation becomes
(3)
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Divide by ,
(4)
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Separating the part,
(5)
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(6)
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(7)
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so
(8)
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which has solution
(9)
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and
(10)
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This can be separated
(11)
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|||
(12)
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so
(13)
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(14)
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These are the Weber differential equations, and the solutions are known as Parabolic Cylinder Functions.
REFERENCES:
Moon, P. and Spencer, D. E. Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd ed. New York: Springer-Verlag, p. 36, 1988.
Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 515 and 658, 1953.
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دواء جديد يعطي الأمل لمرضى الانزلاق الغضروفي
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آلة زمن للمستقبل.."ميتا" تكشف عن نموذج لنظارات الواقع المعزز
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العلاقات العامّة والمجمع العلمي يقيمان محفلًا للمدارس القرآنية من محافظتي النجف والمثنى
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