By Donald D. Fitts
ISBN-10: 0511007639
ISBN-13: 9780511007637
ISBN-10: 0521651247
ISBN-13: 9780521651240
ISBN-10: 0521658411
ISBN-13: 9780521658416
Quantum habit incorporates a huge fraction of recent technological know-how and expertise, together with the legislation of chemistry and the homes of crystals, semiconductors, and superfluids. This graduate-level textual content offers the elemental ideas of quantum mechanics utilizing smooth mathematical suggestions and theoretical ideas, comparable to hermitian operators, Hilbert house, Dirac notation, and ladder operators. the 1st chapters function an creation to quantum conception with a dialogue of wave movement and Schrödinger's wave mechanics. assurance then info the elemental rules of quantum mechanics. all through, simple thought is obviously illustrated and utilized to the harmonic oscillator, angular momentum, the hydrogen atom, the adaptation process, perturbation idea, and nuclear movement. This quantity is the perfect textbook for starting graduate scholars in chemistry, chemical physics, molecular physics and fabrics technology.
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Extra info for Principles of quantum mechanics as applied to chemistry and chemical physics
Sample text
The Born interpretation of jØ(x, t)j2 as the probability density for ®nding the associated particle at position x at time t implies that such a measurement will not yield a unique result. If we have a large number of particles, each of which is in state Ø(x, t) and we measure the position of each of these particles in separate experiments all at some time t, then we will obtain a multitude of different results. We may then calculate the average or mean value hxi of these measurements. In quantum mechanics, average values of dynamical quantities are called expectation values.
11) for the time derivatives of Ø and ØÃ and h pi m obtain 5 Ã 2 2 dh pi À" d Ø dØ d " d Ø V ØÃ À V Ø dx ØÃ 2 dt dx dx dx 2m 2m dx 2 ÀI I À"2 I d 2 ØÃ dØ "2 I Ã d 3 Ø dV dx dx Ø dx À ØÃ Ø 2 3 dx dx 2m ÀI dx dx 2m ÀI ÀI (2X24) I 4 2 2 where the terms in V cancel. I I 2 3 dØÃ dØ d Ø Ã Ã d Ø dx ÀØ Ø dx 2 ÀI dx 3 dx dx ÀI 45 The integrated part vanishes because Ø and dØadx vanish at (Æ) in®nity. 1) has been used. 25) is the quantum analog of Newton's second law of motion, F ma, and is in agreement with the correspondence principle.
What is the group velocity? 19). 3 4 The historical and philosophical aspects of the Copenhagen interpretation are more extensively discussed in J. Baggott (1992) The Meaning of Quantum Theory (Oxford University Press, Oxford). For a derivation, see H. Lamb (1932) Hydrodynamics, pp. 363±81 (Cambridge University Press, Cambridge). 19). 18). 21) and the corresponding function Ø(x, t) obey Parseval's theorem. 1 The SchroÈdinger equation In the previous chapter we introduced the wave function to represent the motion of a particle moving in the absence of an external force.
Principles of quantum mechanics as applied to chemistry and chemical physics by Donald D. Fitts
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