Recent content by JPRitchie
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J
Undergrad 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- JPRitchie
- Post #8
- Forum: Linear and Abstract Algebra
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J
Graduate 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- JPRitchie
- Post #10
- Forum: Linear and Abstract Algebra
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Graduate 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...- JPRitchie
- Post #4
- Forum: Quantum Physics
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Undergrad 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...- JPRitchie
- Post #4
- Forum: Atomic and Condensed Matter
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J
Graduate 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- JPRitchie
- Post #4
- Forum: Atomic and Condensed Matter
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J
Graduate 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...- JPRitchie
- Post #2
- Forum: Atomic and Condensed Matter
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J
Graduate 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...- JPRitchie
- Post #8
- Forum: Thermodynamics
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Graduate 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...- JPRitchie
- Post #6
- Forum: Thermodynamics
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Undergrad 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...- JPRitchie
- Post #9
- Forum: Atomic and Condensed Matter
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Undergrad 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...- JPRitchie
- Post #4
- Forum: Atomic and Condensed Matter
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Graduate Thermal equilibration of a quantum system
That's still pretty vague. I hate guessing games. -Jim- JPRitchie
- Post #13
- Forum: Quantum Physics
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Graduate 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...- JPRitchie
- Post #10
- Forum: Quantum Physics
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Graduate 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...- JPRitchie
- Post #4
- Forum: Quantum Physics
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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... -
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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...