عنوان

Hyperspherical Harmonics :

شابک

9400923236

شابک

9789400923232

شماره

b592837

عنوان اصلي

Hyperspherical Harmonics :

نام عام مواد

[Book]

ساير اطلاعات عنواني

Applications in Quantum Theory

نام نخستين پديدآور

by John Avery.

محل نشرو پخش و غیره

Dordrecht

نام ناشر، پخش کننده و غيره

Springer Netherlands

تاریخ نشرو بخش و غیره

1989

نام خاص و کميت اثر

(XVI, 256 pages).

عنوان فروست

Reidel Texts in the Mathematical Sciences, A Graduate-Level Book Series, 5.

متن يادداشت

Harmonic polynomials --; Generalized angular momentum --; Gegenbauer polynomials --; Fourier transforms in d dimensions --; Fock's treatment of hydrogenlike atoms and its generalization --; Many-dimensional hydrogenlike wave functions in direct space --; Solutions to the reciprocal-space Schrödinger equation for the many-center Coulomb problem --; Matrix representations of many-particle Hamiltonians in hyper spherical coordinates --; Iteration of integral forms of the Schrödinger equation --; Symmetry-adapted hyperspherical harmonics --; The adiabatic approximation --; Appendix A: Angular integrals in a 6-dimensional space --; Appendix B: Matrix elements of the total orbital angular momentum operator --; Appendix C: Evaluation of the transformation matrix U --; Appendix D: Expansion of a function about another center --; References.

متن يادداشت

Where d 3 3)2 (L x - -- i3x j3x j i i>j Thus the Gegenbauer polynomials play a role in the theory of hyper spherical harmonics which is analogous to the role played by Legendre polynomials in the familiar theory of 3-dimensional spherical harmonics; and when d = 3, the Gegenbauer polynomials reduce to Legendre polynomials. The familiar sum rule, in 'lrlhich a sum of spherical harmonics is expressed as a Legendre polynomial, also has a d-dimensional generalization, in which a sum of hyper spherical harmonics is expressed as a Gegenbauer polynomial (equation (3-27»: The hyper spherical harmonics which appear in this sum rule are eigenfunctions of the generalized angular monentum 2 operator A, chosen in such a way as to fulfil the orthonormality relation: VIe are all familiar with the fact that a plane wave can be expanded in terms of spherical Bessel functions and either Legendre polynomials or spherical harmonics in a 3-dimensional space. Similarly, one finds that a d-dimensional plane wave can be expanded in terms of HYPERSPHERICAL HARMONICS xii "hyperspherical Bessel functions" and either Gegenbauer polynomials or else hyperspherical harmonics (equations (4 - 27) and (4 - 30)) : 00 ik·x e = (d-4)!!A~oiA(d+2A-2)j~(kr)C~(~k'~) 00 (d-2)!!I(0) 2: iAj~(kr) 2:Y~ (["2k)Y (["2) A A=O). l). l)J where I(O) is the total solid angle. This expansion of a d-dimensional plane wave is useful when we wish to calculate Fourier transforms in a d-dimensional space.

عنوان اصلي به زبان ديگر

Reidel Texts in the Mathematical Sciences, vol. 5

موضوع مستند نشده

Functions, Special.

موضوع مستند نشده

Physical organic chemistry.

موضوع مستند نشده

Physics.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by John Avery.

مستند نام اشخاص تاييد نشده

John Avery

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y