Elementary Wave Mechanics

W. Heitler, Elementary Wave Mechanics with Applications to Quantum Chemistry, 2nd ed., Oxford University Press, New York, 1969. 

Heitier, W. Elementary Wave Mechanics. Fair Lawn, New Jersey Oxford University Press, 1945. 

Heitler, W. 1956 [1st ed. 1945]. Elementary wave mechanics with applications to chemistry. Oxford Oxford University Press. 

The simple reason for this is now well established quantum mechanics, like relativity, is the nonclassical theory of motion in four-dimensional space-time. All theories, formulated in three-dimensional space, which include Newtonian and wave mechanics, are to be considered classical by this criterion. Wave mechanics largely interprets elementary matter, such as electrons, as point particles, forgetting that the motion of particulate matter needs to be described by particle (Newtonian) dynamics. TF and HF simulations attempt to perform a wavelike analysis and end up with an intractable probability function. On assuming an electronic wave structure, the problem is simplified by orders of magnitude, using elementary wave mechanics. Calculations of this type are weU within the ability of any chemist without expertise in higher mathematics. It has already been shown that the results reported here define a covalence function that predicts, without further assumption, interatomic distances, bond dissociation energies, and harmonic force constants of all purely covalent interactions, irrespective of bond order. In line with the philosophy that... 

According to modern science, all various kinds of matter consist essentially of a few types of elementary particles combined together in different ways. Since these particles do not obey the laws of classical physics but the laws of modern wave mechanics, the problem of the constitution of matter is a quantum-mechanical many-particle problem of a much higher degree of complexity than even the famous classical three-body problem. 

The first two chapters serve as an introduction to quantum theory. It is assumed that the student has already been exposed to elementary quantum mechanics and to the historical events that led to its development in an undergraduate physical chemistry course or in a course on atomic physics. Accordingly, the historical development of quantum theory is not covered. To serve as a rationale for the postulates of quantum theory, Chapter 1 discusses wave motion and wave packets and then relates particle motion to wave motion. In Chapter 2 the time-dependent and time-independent Schrodinger equations are introduced along with a discussion of wave functions for particles in a potential field. Some instructors may wish to omit the first or both of these chapters or to present abbreviated versions. 

Recognizing that many chemistry students do not have a strong background in physics, I have introduced most of the chapters with some essential physics, concerning waves, mechanics, and electrostatics. I have also tried to keep the mathematical level at a minimum, consistent with a proper understanding of what is necessary. Basic calculus and an understanding of the properties of elementary trigonometical and exponential functions are assumed but I have not used complex numbers. Each chapter ends with some simple problems. 

Frank C. Goodrich, A Primer of Quantum Chemistry, Wiley-Interscience, New York, 1972. Heinzwerner Preuss, Quantum Chemistry for Chemists. Elementary Introduction to Its Mathematical and Wave Mechanical Principles, 2nd ed., Verlag Chemie, Weinheim,... 

Elementary quantum mechanics showed that a plane wave exp (iK r) has the same dependence on space and time as the wavefunction of a particle with momentum hK. 

In investigating the highly different phenomena in nature, scientists have always tried to find some fundamental principles that can explain the variety from a basic unity. Today they have shown not only that all the various kinds of matter are built up from a rather limited number of atoms but also that these atoms are composed of a few basic elements or building blocks. It seems possible to understand the innermost structure of matter and its behavior in terms of a few elementary particles electrons, protons, neutrons, photons, etc., and their interactions. Since these particles obey not the laws of classical physics but the rules of modem quantum theory of wave mechanics established in 1925, there has developed a new field of quantum science which deals with the explanation of nature on this basis. 

It follows that a family of trajectories may be obtained by constructing the normals to S, each one distinguished by its starting point x0. This description of particle motion is equivalent to the classic Huygens construction of elementary waves and their envelopes, with mechanical action taking the role of the phase in wave formalism. 

Despite a lot of posturing the electron of chemistry is still the electron of Lewis [53], untouched by quantum electrodynamics (QED). The lip service paid to wave mechanics and electron spin, even in elementary chemistry textbooks, does not alter the fact that the curly arrow of chemistry signifies no more than redistribution of negative charge. By holding out the prospect of an intelligible structure of the electron, quantum mechanics created the expectation that chemistry could be reduced to a subset of physics, explaining all chemical interactions as quantum effects. The result of this unfulfilled... 

These papers present a comprehensive survey of the striking and important recent advances in atomic mechanics. M. Brillouin contributes a detailed and lucid elementary exposition of the Matrix Mechanics of Heisenberg and Dirac. The papers by M. de Broglie include his classical contributions to the new Wave Mechanics, as well as others dealing with Schrbdinger s development of- the idea. 

The intensity of the spectral line is the product of two factors, the irumber of excited atoms and the radiating strength J of an individual atom, which we have just calculated. Thus, with regard to the conditions of excitation of lines, those ideas in Bohr s theory which are brilliantly verified by experiment are just the ideas which are retained in their entirety in the wave mechanics. The latter theory adds a more exact calculation of the intensity J of the individual elementary act, depending on evaluation of the integrals occurring in the matrix elements, while on this question Bohr s theory could only with difficulty make a few statements, with the help of very considerable use of the correspondence principle. 

Enables student with working knowledge of elementary mathematical physics to develop facility in use of quantum mechanics, understand published work in field. Formulates quantum mechanics in terms of Schrocdinger s wave mechanics. Studies evidence for quantum theory, for inadequacy of classical mechanics, 2 postulates of quantum mechanics numerous important, fruitful applications of quantum mechanics in spectroscopy, collision problems, electrons in solids other topics. One of the most rewarding features. .. is the interlacing of problems with text," Amer.. of Physics. Corrected edition. 21 illus. Index. 296pp. 5 x 8. Paperbound 2.00... 

To get a first idea of what density-functional theory is about, it is useful to take a step back and recall some elementary quantum mechanics. In quantum mechanics we learn that all information we can possibly have about a given system is contained in the system s wave function, T. Here we will exclusively be concerned with the electronic structure of atoms, molecules and solids. The nuclear degrees of freedom (e.g., the crystal lattice in a solid) appear only in the form of a potential u(r) acting on the electrons, so that the wave function depends only on the electronic coordinates.2 Nonrelativistically, this wave function is calculated from Schrodinger s equation, which for a single electron moving in a potential v(r) reads... 

The wave model fails to account for phenomena associated W ilh the absorption and emission of radiant energy. I o understand those processes, it is necessary to invoke a particle model in which electromagnetic radiation is viewed as a stream of discrete panicles, or wave packets, of energy called photons. The energy of a photon is proportional to the frequency of the radia turn. ITiese dual views of radiation as particles and as waves are not mutually exclusive bul. rather, cvimple mcniary. Indeed, the wave-panicle duality is found to apply to the behavior of streams of electrons, protons, and other elementary particles and is completely ra-lionali/cd by wave mechanics. 

The harmonic oscillator is treated in practically all elementary books on wave mechanics. See, for example, L. Pauling and E. B. Wilson, Jr., Introduction to (Quantum. Mechanics, Sec. 11, McGraw-Hill, New York, 1935. The original wave inoehanical treatment M as given by E. Schrodinger, Naturwissenschaften, 14 664 (1926). 

According to wave mechanics the most complete statement which is possible about a system is a statement of its wave function, the quantity which appears in Schrodinger s equation. A statement of as u function of the co-ordinates of the elementary partides, is a specification of the quantum state of the system. A great many of... 

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