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The present book contains one hundred and sixty problems, most of them simple, in nonrelativistic quantum mechanics. Some of these problems were used previously by the authors in their courses at the Moscow Institute of Engineering and Physics. However, the majority were drawn up or selected in the course of work on the book. This book is designed for physics students who are studying quantum mechanics approximately at the level of D.I.Blokhintsev's book or Part II of "Theoretical Physics" by A.S.Kompaneyts. A number of problems is intended primarily for students who are beginning to specialize in theoretical physics and who are partially familiar with the contents of "Quantum Mechanics" by L.D.Landau and Ye.M.Lifshits. Some problems illustrate individual theoretical questions which have scarcely been considered in textbooks: sudden and adiabatic changes; Heisenberg representation of operators; probability relations in addition of momenta; isotopic spin; parity; and others. The authors have tried to use relatively elementary mathematical tools of quantum mechanics to facilitate use of the book by nontheoretical physicists. With a few exceptions, the authors have not included in this book problems which are considered in sufficient detail in the basic textbooks mentioned above and in the problem book on quantum mechanics written by V.G.Levich. Therefore, this book should be regarded chiefly as an auxiliary textbook in the study of the above books.
Elementary Methods of Molecular Quantum Mechanics,

Elementary Quantum Mechanics in One Dimension

Elementary Quantum Mechanics in One Dimension

The book consists of ten chapters that present the results of the research work on ionic effect on nucleic acid. The structure and stability of several non-natural triplets are also analysed and comparison has been made with that of natural triplets of nucleic acid. Each chapter explains the objective of the work, and focuses on results and conclusion based on the findings. The thorough explanations of the ab initio method used in the study are included. Both quantum mechanics and molecular mechanics calculations used in the work are illustrated in this chapter.

The book contains the developments in quantum mechanics as well as the basic concepts of quantum formalism in simple terms. Quantum Mechanics is the science of motion of atomic and sub atomic Particles. Experimental measurements for atomic and molecular systems shows that an electron moving around the nucleus of an atom has only a discrete set of values of energy. Rotational motion of particle is of great interest in atomic and molecular problems. For single particle executing such a motion, the Schrodinger equation can be solved. Graduate and senior undergraduate students in Physics, or engineering students, who intend to do research in Physics should find this book useful.

In 1959, physicist Richard Feynman gave a historical lecture “There’s Plenty of Room at the Bottom”. By ‘maneuvering things atom by atom’, he envisioned building smaller and smaller machines, and ultimately using these to build machines at the smallest possible scale. Even after sixty years, the exciting field of nanotechnology is exploding. Over the last few decades, extensive research has been carried out at the atomic scale of matter. Owing to enormous development in high performance computing, computational nanotechnology has exploded in recent years. Because of this, several computing algorithms have been widely used e.g. Monte Carlo Methods (MC), Kinetic Monte Carlo Methods (KMC), and Molecular Dynamics (MD). LAMMPS (“Large-scale Atomic/Molecular Massively Parallel Simulator”), developed by Sandia National Laboratories, has been the ubiquitous for research involving MD. In this book, we have explored some very important and basic problems of Molecular Simulations. All the problems discussed in this book are very fundamental and will develop a strong foundation for advanced research.

Quantum chemistry has emerged in the last two decades as a versatile discipline with its considerable advantages in chemical and material sciences. Concurrently, with the advent of Nanotechnology and the increase in fossil fuel combustion and exhaust emissions, the importance of studying toxic molecules from a sub-molecular view is becoming increasingly important. This book describes the theory behind quantum mechanics, the most used methods of calculation and presents quantum toxicological examinations of nanoparticles and molecular carcinogens that are frequently encountered in polluted natural, rural and urban environments. By the unique blend of quantum sciences and toxicology, the reader is trained in revealing and understanding the toxic properties of molecules from a quantum chemical point of view.

Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be understood, using expansion of the wave function into Fourier integral, that is, on the basis of virtual plane waves. This explanation was proposed by the author in 1963 when the author had been studying Quantum Mechanics. Self-action in a system of elementary particles, charged with elementary charges, is discussed in detail. This self-action is not taken in account in Quantum Mechanics, because otherwise experimental data (including data on atomic spectra) could not be theoretically explained. In Quantum Mechanics sometimes there is an electrostatic field without any electrostatic energy stored in it, and electrostatic negative energy with no charge and no electrostatic field, like in a positronium. Criteria for low-dimensional quantum movements are derived, quantum and classical rotations of modern objects are regarded. Simplified theory of polarons and bipolarins is proposed, and simple explanation of coexistence of zero angular momentum and non-zero magnetic moment in many-electron system is discussed.

Herein the study of inclusion complex of methyl red and cyclodextrins (?, ? and ?-CDs), were investigated using molecular modeling calculation and UV-Vis spectroscopy. The molecular modeling study adopted was docking using Autodock 4.2 software and quantum mechanics calculation using Gaussian 03 software. The UV-Vis spectroscopy results were found to be comparable with the quantum mechanics calculations performed using the semiempirical method PM3. The experimental data (UV, pH, Kb) show that ?-CD is the best host among the studied CD compounds in the following order: MR-?-CD » MR-?-CD » MR-?-CD. Keywords: inclusion complex, ?, ? and ?-cyclodextrins, methyl red.

Flexibility,fragility,emergence of electronic puddles at deformation of graphene are associated with a movement of quantum structures.We used interpretation of quantum mechanics,based on statistical quantum ensembles,and obtained an equation and trajectory for these ensembles,that is, for quantum oscillator,electron orbits which explain reasonably some unusual properties of graphene. In magnetic field,a long-range ordering can be formed by electron structure,named as an united quantum oscillator(UQO),where the number of electrons is correlated with quantum number of oscillator, and the energy per one electron is less than energy of valence electron.This energy difference grows with number of these electrons (as if UQO "attracts" them).This could explain the high conductivity,disorder length scale,formation of clusters: electronic puddles,molecular bond,formation of even a relatively small nebula in space,or of different plasma instabilities which can be as the center of nucleosynthesis.Conditions to start of nucleosynthesis are discussed.Our results could be addressed to students,astrophysicists,experts in nuclear fusion,creators of nanomaterials with desired properties.

The Structure & Interpretation of Quantum Mechanics (Paper)

The book is essentially a result of the authors' attempt to generalize Dirac's elegant method of solving the eigenvalue problem of the linear harmonic oscillator by constructing raising and lowering operators. As such, students of elementary Quantum Mechanics will find Chapters II and III quite useful and illuminating. At many stages in the book the reader will find the power of the commutator algebra unfolding in an elegant manner, as in the original Dirac approach. See the lucid application of the technique to find the eigenvalues and eigenfunctions of the Kratzer oscillator algebraically A student of Advanced Quantum Mechanics will find, in Chapter III, an illustrious application of the celebrated Infeld-Hull factorization method to find a class of ladder operators which connect the eigenstates of a hierarchy of Hamiltonians like, but not the same as, the ones in Supersymmetric Quantum Mechanics. The book will be of interest to a large spectrum of students of Physics at the Master's degree level and graduate students entering a research career in Theoretical Physics and Quantum Chemistry.

The present book contains one hundred and sixty problems, most of them simple, in nonrelativistic quantum mechanics. Some of these problems were used previously by the authors in their courses at the Moscow Institute of Engineering and Physics. However, the majority were drawn up or selected in the course of work on the book. This book is designed for physics students who are studying quantum mechanics approximately at the level of D.I.Blokhintsev's book or Part II of "Theoretical Physics" by A.S.Kompaneyts. A number of problems is intended primarily for students who are beginning to specialize in theoretical physics and who are partially familiar with the contents of "Quantum Mechanics" by L.D.Landau and Ye.M.Lifshits. Some problems illustrate individual theoretical questions which have scarcely been considered in textbooks: sudden and adiabatic changes; Heisenberg representation of operators; probability relations in addition of momenta; isotopic spin; parity; and others. The authors have tried to use relatively elementary mathematical tools of quantum mechanics to facilitate use of the book by nontheoretical physicists. With a few exceptions, the authors have not included in this book problems which are considered in sufficient detail in the basic textbooks mentioned above and in the problem book on quantum mechanics written by V.G.Levich. Therefore, this book should be regarded chiefly as an auxiliary textbook in the study of the above books.

The Picture Book of Quantum Mechanics

This monograph is based on the research done at Department of Physics, DDU Gorakhpur University Gorakhpur,India on unusual DNA structures.Department’s laboratory is pioneer in the field of Computational Modeling, Quantum mechanics and Molecular Mechanics simulations (QM/MM) on bio-molecules. Several high end research articles and theses have been produced during last 10 years form the laboratory. The aim of writing this book is to provide an easy tool/manual to understand nucleic acids, its modeling, QM/MM simulations, conformation and biological functions to the graduate level students and research scholars. This book may also be helpful as a self-study material. Different software and its methodology and compression are also elaborated.

Structure & Interpretation of Quantum Mechanics

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