Recent content by JPRitchie

  1. J

    Eigenvalues & eigenvectors of N x N matrix?

    You might find useful my post at: https://www.physicsforums.com/showthread.php?t=242991 Regards, Jim Ritchie
  2. J

    How to Compute Eigenvectors for Large Matrices Efficiently?

    The area of parallel diagonalization of large matrices is of great interest. To get started, take a look at: http://www.cse.scitech.ac.uk/arc/diags.shtml . If you have additional questions about the software, contact me privately. Jim Ritchie
  3. J

    Understanding Atom Orbital Calculations: Wave Equations, Calculus, and Matrices

    It should be noted that the s,p,d... etc. orbitals you refer to are solutions to the one-electron Schroedinger eqn. only. For atoms and molecules with more electrons, multi-electron systems, no exact closed solutions are known. Nonetheless, multi-electron systems can be approximated using linear...
  4. J

    Can electrostatic forces explain electron configurations?

    TimH: I think the answer to your question is: Yes, BUT you have to use the Schroedinger equation to do it properly. The atomic SE has two terms: one for kinetic energy and one for potential energy. The potential energy term is simply the 1/r function of Coulomb interation - that is...
  5. J

    Electron Density vs Electron Density Difference

    If it were me, I'd use Bader's method. It's quantitative and theoretically sound. Looking only at difference maps can lead to problems. For example, using spherical atoms, one sometimes finds negative differences in covalent systems; flourine molecule is an example. Jim
  6. J

    Electron Density vs Electron Density Difference

    "Electron Density" is usually denoted by the greek symbol rho. Quantum mechanically, it is the number of electrons times the value of the wavefunction times its complex conjugate. In the fields you refer to, values of rho are computed at points on a mesh and then plotted. The electron density is...
  7. J

    Ideal Gas Law for concave objects

    hdyriazi, I was interested in this area a few years ago, but haven't looked at it in a while. A search on amazon with "molecular dynamics" turned up at least a dozen books. Any university science/engineering library will likely have several. More specifically, Erpenbeck did some work on...
  8. J

    Ideal Gas Law for concave objects

    The ideal gas law is based upon atoms/molecules with no volume - point masses. This leads to one of its major flaws: zero volume is predicted at 0K. Other equations of state, van der Waals attempt to remedy this flaw and others through the use of finite molecular volumes. But, there are no...
  9. J

    How Can We Visualize a Hydrogen Atom as a Basketball?

    Donn P, There are so many examples of the kind of thing that you seek that it is hard to know where to start. But, here are my top 3. 1. Computational chemistry - The 1998 Nobel Prize in Chemistry was awarded, in part, to John Pople. He was a principal behind the Gaussian programs. These...
  10. J

    How Can We Visualize a Hydrogen Atom as a Basketball?

    Donn P: The rest mass of the proton is 1836 times larger than that of the electron. This large difference is the basis some important equations, such as the Born-Oppenheimer equation. So having a qualitative knowledge of the realtive sizes of things can result in quantitative advances...
  11. J

    Thermal equilibration of a quantum system

    That's still pretty vague. I hate guessing games. -Jim
  12. J

    Thermal equilibration of a quantum system

    You're being too vague. If you don't include all the real effects I mentioned that are possible in your simulation, your simulation won't be realistic. You'll have GIGO. If you're trying to simulate a reasonably dense gas or liquid or other disordered state, symmetry considerations may not...
  13. J

    Thermal equilibration of a quantum system

    This is not always a correct statement - witness absorption and emission spectra, especially for the hydrogen atom, explanations of the line spectra for which led to the postulation of energy quantization. Also, remember there are electronic, vibrational, and rotational degrees of freedom...
  14. J

    What Happens to the Water Produced During Fuel Combustion?

    Nothing about this thread makes a lot of sense. See the wiki entry for heat of combustion and calorimeter for basic information, as well as other common thermodynamic quantities. Water does frequently have anamolous properties, because of hydrogen bonding. For example, the wiki has some...
  15. J

    MO Theory, sp Hybridization question

    The out-of-phase lobe of an sp hybrid is smaller than the in-phase lobe, but not infinitesimally small. It's needed to maintain orthogonality between different hybrids on the same atom. That is, the properly normalized sum and difference of an s and p orbital gives two sp hybrids that are...
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