Skip to content

Download A New Crystal for Wave-Length Measurements of Soft X-Rays by Pauling L. PDF

By Pauling L.

Show description

Read or Download A New Crystal for Wave-Length Measurements of Soft X-Rays PDF

Best quantum physics books

The Quantum Universe: Everything That Can Happen Does Happen

The Quantum Universe brings jointly authors on a brilliantly bold challenge to teach that everybody can comprehend the private questions of technology. yet simply what's quantum physics? How does it aid us comprehend the area? the place does it go away Newton and Einstein? And why, chiefly, do we ensure the idea is sweet?

Quantum Description of High-Resolution NMR in Liquids

This e-book describes the most equipment of 1- and two-dimensional high-resolution nuclear magnetic resonance spectroscopy in beverages in the quantum-mechanical formalism of the density matrix. In view of the expanding value of NMR in chemistry and biochemistry, the paintings is especially addressed to these scientists who don't have a operating wisdom of quantum calculations.

Additional info for A New Crystal for Wave-Length Measurements of Soft X-Rays

Example text

1 Rigid diatomic molecule As a pilot example let us consider the quantum mechanics of a rigid diatomic molecule with nuclear masses m1 and m2 , and (equilibrium) bond length, Re (see figure). Since the molecule is rigid, its coordinates can be specified by 2 r2 its centre of mass, R = m1mr11 +m +m2 , and internal orientation, r = r2 − r1 (with |r| = Re ). 1) ˆ = −i ∇R and L ˆ =r×p ˆ denotes the angular momentum associated where P with the internal degrees of freedom. Since the internal and centre of mass degrees of freedom separate, the wavefunction can be factorized as ψ(r, R) = eiK·R Y (r), where the first factor accounts for the free particle motion of the body, and the second factor relates to the internal angular degrees of freedom.

The ground state wavefunction is therefore spherically symmetric, and the function w(ρ) = w0 is just a constant. Hence u(ρ) = ρe−ρ w0 and the actual radial wavefunction is this divided by r, and of course suitably normalized. To write the wavefunction in terms of r, we need to find κ. 2 1 With this definition, the energy levels can then be expressed as En = − 4π1 0 (Ze) 2a0 n2 . Moving on to the excited states: for n = 2, we have a choice: either the radial function w(ρ) can have one term, as before, but now the angular momentum = 1 (since n = k + + 1); or w(ρ) can have two terms (so k = 1), and = 0.

4. ATOMIC HYDROGEN 40 To further simplify the wave equation, it is convenient to introduce the dimensionless variable ρ = κr, leading to the equation ∂ρ2 u(ρ) = 1− 2ν ( + 1) + ρ ρ2 u(ρ) , where (for reasons which will become apparent shortly) we have introduced Ze2 κ . Notice that in transforming from r the dimensionless parameter ν = 4π 0 2E to the dimensionless variable ρ, the scaling factor depends on energy, so will be different for different energy bound states! Consider now the behaviour of the wavefunction near the origin.

Download PDF sample

Rated 4.05 of 5 – based on 23 votes