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.

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.

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.

scholarly journals NEW FEATURES IN SUPERSYMMETRY BREAKDOWN IN QUANTUM MECHANICS

1996 ◽  
Vol 11 (19) ◽  
pp. 1563-1567 ◽  
Author(s):  
BORIS F. SAMSONOV
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Mechanical Model ◽  
State Energy ◽  
Vacuum State ◽  
Quantum Mechanical ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Quantum Mechanical Model ◽  
Higher Derivative

The supersymmetric quantum mechanical model based on higher-derivative supercharge operators possessing unbroken supersymmetry and discrete energies below the vacuum state energy is described. As an example harmonic oscillator potential is considered.

scholarly journals CONSISTENT DEFORMED BOSONIC ALGEBRA IN NONCOMMUTATIVE QUANTUM MECHANICS

2008 ◽  
Vol 23 (09) ◽  
pp. 1393-1403 ◽  
Author(s):  
JIAN-ZU ZHANG
Keyword(s):  
Quantum Mechanics ◽  
Weyl Algebra ◽  
Fock Space ◽  
General Relation ◽  
Noncommutative Space ◽  
Two Dimensional ◽  
Noncommutative Quantum Mechanics ◽  
Commutative Space ◽  
Creation Operators ◽  
Noncommutative Quantum

In two-dimensional noncommutative space for the case of both position–position and momentum–momentum noncommuting, the consistent deformed bosonic algebra at the nonperturbation level described by the deformed annihilation and creation operators is investigated. A general relation between noncommutative parameters is fixed from the consistency of the deformed Heisenberg–Weyl algebra with the deformed bosonic algebra. A Fock space is found, in which all calculations can be similarly developed as if in commutative space and all effects of spatial noncommutativity are simply represented by parameters.

scholarly journals ADELIC HARMONIC OSCILLATOR

1995 ◽  
Vol 10 (16) ◽  
pp. 2349-2365 ◽  
Author(s):  
BRANKO DRAGOVICH
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Functional Relation ◽  
Vacuum State ◽  
One Dimensional ◽  
High Energies ◽  
The Riemann Zeta Function ◽  
Adelic Quantum Mechanics ◽  
Riemann Zeta ◽  
Very High

Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered. It is a simple, exact and instructive adelic model. Eigenstates are Schwartz-Bruhat functions. The Mellin transform of the simplest vacuum state leads to the well-known functional relation for the Riemann zeta function. Some expectation values are calculated. The existence of adelic matter at very high energies is suggested.

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