Download Angular Momentum Theory for Diatomic Molecules by Brain Judd (Auth.) PDF

By Brain Judd (Auth.)

Show description

Read or Download Angular Momentum Theory for Diatomic Molecules PDF

Best quantum theory books

Deep beauty. Understanding the quantum world through mathematical innovation

No medical idea has triggered extra puzzlement and confusion than quantum idea. Physics is meant to assist us to appreciate the area, yet quantum thought makes it look a truly unusual position. This ebook is set how mathematical innovation might help us achieve deeper perception into the constitution of the actual international.

Path Integrals in Quantum Mechanics

The most target of this paintings is to familiarize the reader with a device, the trail necessary, that provides an alternate perspective on quantum mechanics, yet extra vital, lower than a generalized shape, has develop into the foremost to a deeper figuring out of quantum box concept and its functions, which expand from particle physics to section transitions or homes of quantum gases.

Additional info for Angular Momentum Theory for Diatomic Molecules

Sample text

30) is a n example of a Fredholm equation of t h e second kind [ 3 8 ] . T h e general m e t h o d for solving such a n equation is t o e x p a n d b o t h kernel a n d function in some series of orthonormal polynomials, thereby obtaining a series of equations for t h e coefficients in t h e expansion of t h e function. T h e n a t u r a l choice for our polynomials is t h e four-dimen­ sional spherical harmonics. If we specialize t o t h e hydrogen a t o m , we can set R = 0, corresponding t o a charge Ze a t t h e origin.

1). Freed [ 3 4 ] has described in detail the procedures to follow when the method of reversed angular momentum is adopted. It is not necessary to take Van Vleck's extreme position. Carrington et al. 8) can be corrected by setting V = V> λ / = — λ,", V = , V i for then λ" satisfies the commutation relations of an ordinary angular momentum vector. Alternatively, all these adjustments can be avoided b y accepting Eq. 7), and this is the course we shall follow here. 2). 3 REDUCED MATRIX ELEMENTS An important matrix element for eigenstates of the rigid rotator is (JMN I Dp™ I J'M'N').

I t is n o t difficult t o show t h a t 2 ΚΛοο(Ω) = 1 2 ( 2 7 T ) - / C n - l ( C O S X) . Furthermore, r 2(rc-l) \ W (nOO, n'00 | n " 0 0 ) = (00, 00 | 00) η" i(n = (η'ΥηηΟ^Δίη - #/ 0 - 1) i(n' - 1) 0 - 1) h(n" 1) 0 1, n' - 1, n " - 1), where Δ = 1 if t h e t r i a d (n — 1, n' — 1, η " — 1) satisfies t h e t r i a n g u l a r condition a n d if, in addition, η + n' + n" is o d d : otherwise Δ = 0. 7. So E q . 31) becomes 2 C w- i ( c o s x ) C n ' - i ( c o s x ) = Σ f m {2τ η"/nn ) f(nn'n") n" X A(n - 1, n' - 1, n " - l ) C n - - i ( c o s X) .

Download PDF sample

Rated 4.57 of 5 – based on 5 votes