Ideas of Quantum Chemistry P94 pptx

... independence. A set of vectors is called a set of linearly independent vec- tors if no vector of the set can be expressed as a linear combination of the other vectors of the set. The number of linearly ... or- thogonal. The number of linearly independent eigenvectors which correspond to a given eigenvalue a is called the degree of degeneracy of the eigenvalue. Such vectors d...

Ngày tải lên: 06/07/2014, 09:20

... is mean value of measurements Fig. 1.9. The results of measurements of a quantity A are the eigenvalues of the operator ˆ A: E 1 and E 2 . Postulate V (spin angular momentum) spin Spin of elementary ... systems. 16 1. The Magic of Quantum Mechanics moving along a single coordinate axis x (the mathematical foundations of quantum mechanics are given in Appendix B on p. 895). P...

Ngày tải lên: 06/07/2014, 09:20

... and some of the inequalities they have to fulfil. The the- orem pertains to the basic logic of the measurements and is valid independently of the kind of particles and of the nature of their interaction. ... Copenhagen for quantum mechanics was like Rome for catholics, and Bohr played the role of the president of the Quantum Faith Con- gregation. 52 The picture of the wor...

Ngày tải lên: 06/07/2014, 09:20

... abyss of the sea without a bottom. 22 The presence of the Dirac sea makes the Dirac the- ory, in fact, a theory of an infinite number of particles, whereas formally it was only a theory of a single ... CALCULATION OF THE GROUND STATE OF THE HYDROGEN-LIKE ATOM WITHIN DIRAC THEORY Matrix form of the Dirac equation We will use the Dirac equation (3.59). First, the basis set compos...

Ngày tải lên: 06/07/2014, 09:20

... disposal all the necessary solutions of eq. (5.16). The eigenfunctions of the ˆ H (0) operator appeared as a consequence of using them as the complete set of functions (e.g., in expanding ψ (1) k ). ... ψ k (λ) are analytical functions of λ (p. 205). In this mathematical aspect of the physical problem we may treat λ as a complex number. Then the radius of convergence ρ of the...

Ngày tải lên: 06/07/2014, 09:20

... has to be convex as a function of the positions of the nuclei. 6. Please choose the wrong answer. As a result of the rotational excitation J → (J +1) of a molecule of length R: a) the angular momentum ... func- tion in the form of a product of an electronic function and a function describing the motion of the nuclei; c) leads to the notion of the potential energy curve for t...

Ngày tải lên: 06/07/2014, 09:20

... bond One of the molecules is a donor, the other is an acceptor of a proton, Fig. 7.10.a. A local minimum of smaller stability appears when one of the water molecules serves as a donor of two protons, ... 7.10.a): • stretchingofthehydrogenbondO–H O(thevibrationoftwowatermolecules treated as entities): 183 cm −1 • bendingofthehydrogenbondO–H Ointheplaneofthefigure:345cm −1 • bendingoft...

Ngày tải lên: 06/07/2014, 09:20

... correlation of motion of some atoms or groups of atoms, i.e. the space correlation (“when this group of atoms is shifted to correlation and auto-correlation the left, then another group is most often ... (1953) 1087. 314 7. Motion of Nuclei (sometimes it takes months on the fastest computers of the world) and calculat- ing statistics of the number of accepted conformations as...

Ngày tải lên: 06/07/2014, 09:20

... professor of Mathe- matics at Queen’s College in Cork and a member of the Royal Society. In 1854 Boole wrote his Opus Magnum “ An Investigation of the Laws of Thought ”, creating a domain of ... interval has to be decreased by a factor of 10 (i.e. 0.1 fs instead of 1 fs), which allows us to reach simulation times of the order of 10–100 picoseconds instead of (in classical...

Ngày tải lên: 06/07/2014, 09:20

... sign, not of the strength of quantum chemistry, but of its weakness. What are we going to do with such a function? We may load it back into the com- puter and calculate all the properties of the ... results, we need to include a large number of determi- nants, e.g., of the order of thousands, millions or even billions. 52 This means that contemporary quantum chemistry has...

Ngày tải lên: 06/07/2014, 09:20