April 24, 2016, 11:10 a.m.

H2 Energy computed with GTO

Results

E = -1.8706052190703892 Ry

R = 1.4186131

Sept. 26, 2015, 2:04 p.m.

DFT

Density functional theory is a computational quantum mechanical modelling method to investigate the electronic structure (principally the ground state) of many-body systems. Computational costs are relatively low when compared to traditional methods, such as Hartree–Fock theory and its descendants based on the complex many-electron wavefunction.

Aug. 27, 2015, 10:15 a.m.

Computed overlap integral via STOnG

STOnG is basis set for GTO that maps Slater's orbital. Thanks to Gaussian Product Rule GTO are more computationly efficient.

Aug. 17, 2015, 6:20 a.m.

Gaussian Product Rule

The product of two Gaussian functions located on different centers is a new Gaussian function located on a new center. Four-center electron distributions could be reduced to a single-center distributions.

Philip E. HOGGAN "Molecular Integrals over Slater-type Orbitals. From pioneers to recent progress"

June 25, 2015, 6:45 a.m.

STO - Slater-type orbital

Slater type orbital is a mathematic function that describes wave-like behaviour of the electrons in an atom. STOs has no radial nodes. Slater orbitals are the natural basis functions in quantum molecular calculations. Their use has been rather restricted, mostly due to mathematical integration difficulties.

P.E. Hoggan, M.B. Ruiz, and T. Özdogan, Molecular Integrals over Slater-type orbitals. From pioneers to recent progress, in Quantum Frontiers of Atoms and Molecules

June 21, 2015, 9:16 a.m.

The importance of eigenvalues

Eigenvectors make understanding linear transformations easy. They are the "axes" (directions) along which a linear transformation acts simply by "stretching/compressing" and/or "flipping"; eigenvalues give you the factors by which this compression occurs.

http://math.stackexchange.com/questions/23312/what-is-the-importance-of-eigenvalues-eigenvectors

Oct. 28, 2014, 7:48 a.m.

Numerical integration of improper divergent integrals

Computing integrals using Monte Carlo methods and going further with MISER adaptive algorithm. Trying importance sampling. http://http://scikit-monaco.readthedocs.org

May 15, 2014, 10:33 p.m.

Philosophical implications of QM

The basis of a science is its ability to predict. To predict means to tell what will happen in an experiment that has never been done. Given an arbitrary accuracy, no matter how precise, one can find a time long enough that we cannot make predictions valid for that long a time.

May 15, 2014, 10:24 p.m.

Relativistic Doppler effect

Change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer.

May 2, 2014, 12:24 p.m.

Quantum mechanics - predicting

Quantum mechanics is a predictive theory, not just measurements after the fact. So we must talk about what we can predict, not only what we've already known on the beginning of the experiment.

March 16, 2014, 9:35 p.m.

Momentum in qunatum mechanics

p =  − iℏ∇

March 12, 2014, 11:04 p.m.

Annihilation in decimal state form

Translating Ket state to binary and then shorten it in decimal form, requires fast method for creation, annihilation for selected node. The value of with the state should by changed can be obtain throughout equation:

22n − 2i + 1 − spin
n − quantityofnodes
i − nodenumber
spin − ↑:0↓:1

March 11, 2014, 8:08 p.m.

How to Read an Academic Article

  1. Read the abstract
  2. Read the introduction.
  3. Read the conclusion.
  4. Skim the middle, looking at section titles, tables, figures.
  5. Read the whole thing quickly, skipping equations, most figures and tables.
  6. Read the whole thing carefully, focusing on the sections or areas that seem most important.

http://organizationsandmarkets.com/2010/08/31/how-to-read-an-academic-article/

March 9, 2014, 10:02 a.m.

Numpy scipy - Use case

Np.array manipulation, model building, approximation and plotting.

http://pypix.com/scientific/machine-learning-python/

March 3, 2014, 8:42 p.m.

Eigenvalues testing

Av = λv
vals, vectors = eigs(A)
l = vals[0]
v = vectors[:, 0]

assert allclose(A * l, l * v)

http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

March 2, 2014, 11:39 p.m.

Hooke's law

General tensor form

http://en.m.wikipedia.org/wiki/Hooke's_law

Feb. 25, 2014, 6:25 p.m.

Reclaim memory from sympy

sympy.core.cache.clear_cache()

https://github.com/sympy/sympy/wiki/Faq#wiki-how-do-i-clear-the-cache