1 On the N - dimensional hydrogen atom in momentum representation
نویسنده
چکیده
We derive the wave function for N-dimensional hydrogen atom in the momentum representation with the phase factor using the generating function method and Hankel’s integral.
منابع مشابه
The two-dimensional hydrogen atom in The momentum representation
The analytic expression of the momentum representation in terms of the associated Legendre function is determined by a direct integration of Fourier transform of the wave function of coordinates using the Levi-Civita transformation and 2 2 R R → the generating function method. A new generating function for the associated Legendre functions are obtained.
متن کاملDFT-PBE, DFT-D, and MP2 Studies on the H2O•••HNH and HOH•••NH2 Hydrogen Bonds in Water-Aniline Complexes
DFT-GGA method of Perdew-Burke-Ernzerhof (PBE) is used with aug-cc-PVTZ, 6-311++G**, and Def2-TZVP large basis sets to study the hydrogen bond interactions between oxygen lone pair as a donor electron with hydrogen atom connected to the aniline’s nitrogen as an electron acceptor (H2O···HNH-Ph), and nitrogen lone pair with hydrogen of water molecule (Ph-H2N···HOH...
متن کاملFunctionals of Gegenbauer Polynomials and D-dimensional Hydrogenic Momentum Expectation Values 1
The system of Gegenbauer polynomials fC n (x); n = 0; 1; : : :g is a classical family of polynomials orthogonal with respect to the weight function ! (x) = (1?x 2) ? 1 2 on the support interval ?1; +1]. Integral functionals of Gegenbauer polynomials with kernel f(x))C n (x)] 2 ! (x), where f(x) is an arbitrary function which does not depend on n or , are considered in this paper. Firstly, a gen...
متن کاملHydrogen Adsorption on (5,0) and (3,3) Na-decorated BNNTs
The storage capacity of hydrogen on Na-decorated born nitride nanotubes (BNNTs) is investigated by using density functional theory within Quantum Espresso and Gaussian 09. The results obtained predict that a single Na atom tends to occupy above the central region of the hexagonal rings in (5,0) and (3,3) BNNT structures with a binding energy of -2.67 and -4.28 eV/Na-atom respectively. When a si...
متن کاملOn the hydrogen wave function in Momentum-space, Clifford algebra and the Generating function of Gegenbauer polynomial
Using the quadratic transformation and the generating function method we 3 4 R R → perform the Fourier transformation of the wave function of coordinates of hydrogen atom and we find the analytic expression of the wave function in momentum space. We derive the matrix elements between the basis to 4-dimensions and integral representation of the generating functions of Gegenbauer polynomials. We ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009