scholarly journals Uma introdução à Teoria Quântica de muitas partículas aplicada a Física do Estado Sólido

1992 ◽  
Vol 14 (14) ◽  
pp. 35
Author(s):  
José Antônio Trindade Borges da Costa
Keyword(s):  
State Physics ◽  
Quantum Mechanics ◽  
Occupation Number ◽  
Particle Systems ◽  
Collective Excitations ◽  
Number Representation ◽  
Solid State Physics ◽  
General Representation ◽  
Second Quantization ◽  
The Many

Some fundamental concepts and mathematical tools of the quant um theory of many particle systems, which are indispensable to the study of solid state physics. are presented. The concepts of collective excitations and quasi-particles are stressed. Concerning the mathematical tools, Quantum Mechanics is presented in its general, representation independent formalism. The many-particle problem is approached in the occupation number representation, or second quantization. Finally, as an application the interaction between electrons and the vibrations of a crystal lattice, described in terms of elementary excitations of collective waves, i.e., phonons, is expressed and discussed within this framework.

Quantum Many-Particle Systems and Second Quantization

2019 ◽  
pp. 5-44
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Mathematical Formulation ◽  
Particle Systems ◽  
Quantum Field ◽  
Second Quantization ◽  
Creation And Annihilation Operators ◽  
Quantum Matter ◽  
Interacting Systems ◽  
The Many

Chapter 2 provides a review of pertinent aspects of the quantum mechanics of systems composed of many particles. It focuses on the foundations of quantum many-particle physics, the many-particle Hilbert spaces to describe large assemblies of interacting systems composed of Bosons or Fermions, which lead to the versatile formalism of second quantization as a convenient and eminently practical language ubiquitous in the mathematical formulation of the theory of many-particle systems of quantum matter. The main objects in which the formalism of second quantization is expressed are the Bosonic or Fermionic creation and annihilation operators that become, in the position basis, the quantum field operators.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

Memories of early days in solid state physics

1980 ◽  
Vol 371 (1744) ◽  
pp. 56-66 ◽  
Keyword(s):  
State Physics ◽  
Quantum Mechanics ◽  
Solid State ◽  
Nobel Prize ◽  
Niels Bohr ◽  
Theoretical Physics ◽  
Solid State Physics ◽  
Research Papers ◽  
Atomic Collisions

Mott, Sir Nevill. Born Leeds 1905. Studied theoretical physics under R. H. Fowler in Cambridge, in Copenhagen under Niels Bohr and in Gottingen. Professor of Theoretical Physics in Bristol 1933-54, and Cavendish Professor of Physics, Cambridge 1954-71. Nobel Prize for Physics 1977. Author of several books and research papers on application of quantum mechanics to atomic collisions and since 1933 on problems of solid state science

scholarly journals COMPLEX RATIONAL NUMBERS IN QUANTUM MECHANICS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1730-1741
Author(s):  
PAUL BENIOFF
Keyword(s):  
Quantum Mechanics ◽  
Occupation Number ◽  
Vacuum State ◽  
Rational Numbers ◽  
Integer Lattice ◽  
Binary Representation ◽  
Number Representation ◽  
Creation Operators

A binary representation of complex rational numbers and their arithmetic is described that is not based on qubits. It takes account of the fact that 0s in a qubit string do not contribute to the value of a number. They serve only as place holders. The representation is based on the distribution of four types of systems, corresponding to +1, -1, +i, -i, along an integer lattice. Complex rational numbers correspond to arbitrary products of four types of creation operators acting on the vacuum state. An occupation number representation is given for both bosons and fermions.

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