scholarly journals Introducing Viewpoints of Mechanics into Basic Growth Analysis-(XII) : Applying Sign Reversal of Phase, Space Inversion and Time Reversal to Wave Functions with Negative Amplitude-

10.5109/16115 ◽  
2009 ◽  
Vol 54 (2) ◽  
pp. 357-359
Author(s):  
Masataka Shimojo
Keyword(s):  
Phase Space ◽  
Time Reversal ◽  
Growth Analysis ◽  
Wave Functions ◽  
Sign Reversal ◽  
Space Inversion

scholarly journals Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
H. Panahi ◽  
A. Savadi
Keyword(s):  
Exact Solution ◽  
Phase Space ◽  
Algebraic Approach ◽  
Wave Functions ◽  
Dirac Oscillator ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues ◽  
Good Agreement

We study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl(2) algebraization. It is shown that the results are in good agreement with those obtained previously via a different method.

Operators, Matrix Elements, and Wave Functions under Time-Reversal Symmetry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Quantum Chemistry ◽  
Time Reversal ◽  
Relativistic Quantum ◽  
Spin Symmetry ◽  
Computational Effort ◽  
Wave Functions ◽  
Time Reversal Symmetry ◽  
Molecular Systems ◽  
Self Consistent Field ◽  
Relativistic Quantum Chemistry

We now take on the task of developing the theory and methods for a relativistic quantum chemistry. The aim is to arrive at a qualitative as well as a quantitative understanding of the relativistic effects in molecules. We must be able to predict the effects of relativity on the wave functions and electron densities of molecules, and on the molecular properties arising from these. And we must develop methods and algorithms that enable us to calculate the properties and interactions of molecules with an accuracy comparable to that achieved for lighter systems in a nonrelativistic framework. Parts of this development follow fairly straightforwardly from our considerations of the atomic case in part II, but molecular systems represent challenges of their own. This is particularly true for the computational techniques. From the nonrelativistic experience we know that present-day quantum chemistry owes much of its success to the enormous effort that has gone into developing efficient methods and algorithms. This effort has yielded powerful tools, such as the use of basis-set expansions of wave functions, the exploitation of molecular symmetry, the description of correlation effects by calculations beyond the mean-field approximation, and so on. In developing a relativistic quantum chemistry, we must be able to reformulate these techniques in the new framework, or replace them by more suitable and efficient methods. In nonrelativistic theory, spin symmetry provides one of the biggest reductions in computational effort, such as in the powerful and elegant Graphical Unitary Group Approach (GUGA) for configuration interaction (CI) calculations (Shavitt 1988). For relativistic applications, time-reversal symmetry takes the place of spin symmetry, and this chapter is devoted to developing a formalism for efficient incorporation of this symmetry in our theory and methods. Time-reversal symmetry includes the spin symmetry of nonrelativistic systems, but there are significant differences from spin symmetry for systems with a Hamiltonian that is spin-dependent. The development of techniques that incorporate time-reversal symmetry presented here are primarily aimed at four-component calculations, but they are equally applicable to two-component calculations in which the spin-dependent operators are included at the self-consistent field (SCF) stage of a calculation.

scholarly journals Phase-space manipulations of many-body wave functions

2014 ◽  
Vol 90 (6) ◽  
Author(s):  
G. Condon ◽  
A. Fortun ◽  
J. Billy ◽  
D. Guéry-Odelin
Keyword(s):  
Phase Space ◽  
Body Wave ◽  
Wave Functions ◽  
Many Body

scholarly journals Realization of the noncommutative Seiberg–Witten gauge theory by fields in phase space

2015 ◽  
Vol 30 (22) ◽  
pp. 1550135 ◽  
Author(s):  
R. G. G. Amorim ◽  
F. C. Khanna ◽  
A. P. C. Malbouisson ◽  
J. M. C. Malbouisson ◽  
A. E. Santana
Keyword(s):  
Hilbert Space ◽  
Gauge Theory ◽  
Phase Space ◽  
Gauge Symmetry ◽  
Probability Density ◽  
Symmetry Analysis ◽  
Wave Functions ◽  
Wigner Functions ◽  
Poincaré Symmetry

Representations of the Poincaré symmetry are studied by using a Hilbert space with a phase space content. The states are described by wave functions (quasi-amplitudes of probability) associated with Wigner functions (quasi-probability density). The gauge symmetry analysis provides a realization of the Seiberg–Witten gauge theory for noncommutative fields.

scholarly journals Некоммутативная задача Ландау о фазовом пространстве при наличии минимальной длины

2020 ◽  
pp. 188-198
Author(s):  
F.A. Dossa ◽  
J.T. Koumagnon ◽  
J.V. Hounguevou ◽  
G.Y.H. Avossevou
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Momentum Space ◽  
Hypergeometric Functions ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Uvarov Method

The deformed Landau problem under a electromagnetic field is studied, where the Heisenberg algebra is constructed in detail in non-commutative phase space in the presence of a minimal length. We show that, in the presence of a minimal length, the momentum space is more practical to solve any problem of eigenvalues. From the Nikiforov-Uvarov method, the energy eigenvalues are obtained and the corresponding wave functions are expressed in terms of hypergeometric functions. The fortuitous degeneration observed in the spectrum shows that the formulation of the minimal length complements that of the non-commutative phase space. Изучается деформированная задача Ландау в электромагнитном поле, в которой алгебра Гейзенберга подробно строится в некоммутативном фазовом пространстве при наличии минимальной длины. Мы показываем, что при наличии минимальной длины импульсное пространство более практично для решения любой проблемы собственных значений. С помощью метода Никифорова-Уварова получаются собственные значения энергии, а соответствующие волновые функции выражаются через гипергеометрические функции. Случайное вырождение, наблюдаемое в спектре, показывает, что формулировка минимальной длины дополняет формулировку некоммутативного фазового пространства.

Matrices and Wave Functions under Double-Group Symmetry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Time Reversal ◽  
Point Group ◽  
Computational Effort ◽  
Wave Functions ◽  
Group Symmetry ◽  
Time Reversal Symmetry ◽  
Point Group Symmetry ◽  
Matrix Elements ◽  
Double Group

Symmetry is one of the most versatile theoretical tools of physics and chemistry. It provides qualitative insight into the wave functions and properties of systems, and it has also been used successfully to obtain great savings in computational efforts. In the preceding chapter we examined time-reversal symmetry, and now we turn to the more familiar point-group symmetry. We show how relativity requires special consideration and extensions of the concepts developed for the nonrelativistic case, and how time-reversal symmetry and double-group symmetry are connected. Although the techniques that incorporate double-group symmetry presented here are primarily aimed at four-component calculations, they are equally applicable to two-component calculations in which the spin-dependent operators are included at the SCF stage of a calculation. In the preceding chapter, we have shown how the use of time-reversal symmetry can lead to considerable reduction in the number of unique matrix elements that appear in the operator expressions. However, we are also interested in the overall structure of the matrices of the operators. In particular, we are interested in possible block structures, where classes of matrix elements may be set to zero a priori. If the matrices can be cast in block diagonal form, we may save on storage as well as computational effort in solving eigenvalue problems, for example. Matrix blocking will already be effected by the point-group symmetry of the molecule.

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