Register to reply

Hamiltonian in atomic units

by Shadowz
Tags: atomic, hamiltonian, units
Share this thread:
Shadowz
#1
Feb18-11, 01:03 AM
P: 43
1. The problem statement, all variables and given/known data
So the question is I have to use some trial function of the form [tex]\sum c_if_i[/tex] to approximate the energy of hydrogen atom where [tex]f_i=e^{-ar}[/tex] for some number a (positive real number). Note that r is in atomic unit.

2. Relevant equations
Because r is in atomic unit, I think I should use the Hamiltonian in atomic unit, that is
[tex]H = -\frac{1}{2}\nabla^2 + \frac{1}{r}[/tex]
or should I use the spherical Hamiltonian?

I try to compute [tex]H_{ij} = \int_0^\infty f_iHf_j[/tex] but there will be the term [tex]\int_0^\infty f_1\frac{1}{r}f_2dr[/tex] which cannot be integrated (not converged). So what's wrong with the way I approach the problem?

Thank you,
Phys.Org News Partner Science news on Phys.org
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
sgd37
#2
Feb18-11, 03:06 AM
P: 205
might your coefficients be r dependent since they are in the full solution of the hydrogen like atom
asheg
#3
Feb23-11, 02:59 PM
P: 51
[tex]
\int_0^\infty f_1\frac{1}{r}f_2dr
[/tex]
will converge if you change 1/r to 1/(r+eps)


Register to reply

Related Discussions
Tunnel ionization rates; question on atomic units Advanced Physics Homework 3
Energy levels of hydrogen in atomic units Advanced Physics Homework 0
Atomic mass units Chemistry 1
Using atomic units Introductory Physics Homework 1
Atomic Mass Units Introductory Physics Homework 3