ENERGY SPECTRAL STATISTICS IN THE QUANTUM SYSTEM WITH TWO PARTICLES

In this paper, the quantum system with two particles is analyzed and the energy level spacing statistics distribution and Δ3-statistic are given. The results show that hard quantum chaos appear in the system with a certain potential. Tunnelling effect develops quantum chaos.

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ENERGY LEVEL QUASI-CROSSINGS: ACCIDENTAL DEGENERACIES OR SIGNATURE OF QUANTUM CHAOS?

International Journal of Modern Physics E ◽

10.1142/s0218301300000283 ◽

2000 ◽

Vol 09 (04) ◽

pp. 279-297

Author(s):

V. R. MANFREDI ◽

L. SALASNICH

Keyword(s):

Energy Level ◽

Quantum Chaos ◽

Energy Levels ◽

Classical Dynamics ◽

Spectral Statistics

In the field of quantum chaos, the study of energy levels plays an important role. The aim of this review is to critically discuss some of the main contributions regarding the connection between classical dynamics, semi-classical quantization and spectral statistics of energy levels. In particular, we analyze in detail degeneracies and quasi-crossings in the eigenvalues of quantum Hamiltonians which are classically non-integrable.

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QUANTUM CHAOS IN NON-SYMMETRIC POTENTIAL WELL IN A TILTED MAGNETIC FIELD

International Journal of Modern Physics B ◽

10.1142/s0217979204026032 ◽

2004 ◽

Vol 18 (17n19) ◽

pp. 2752-2756 ◽

Cited By ~ 1

Author(s):

GUOYONG YUAN ◽

SHIPING YANG ◽

HONGLING FAN ◽

HONG CHANG

Keyword(s):

Magnetic Field ◽

Quantum Chaos ◽

Chaotic Behavior ◽

Dynamical Behavior ◽

Potential Well ◽

Symmetric Potential ◽

Tunnelling Effect ◽

Non Linear ◽

Spectral Statistics ◽

Tilted Magnetic Field

In this paper, the dynamical behavior of a non-symmetric double potential well in a tilted magnetic field is studied. The classical Poincare section is given to exhibit the chaotic behavior of the system, and non-linear resonant lead to chaos. The paper has also given the energy spectral statistics which satisfies Brody's distribution, tunnelling effect develops quantum chaos and also holds back the development of chaos.

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Quantum Boxes, Stringed Instruments

10.1093/oso/9780198808275.003.0008 ◽

2017 ◽

Author(s):

Frank S. Levin

Keyword(s):

Energy Level ◽

Schrödinger Equation ◽

Quantum System ◽

Schrodinger Equation ◽

Probability Distributions ◽

Wave Functions ◽

Energy Level Diagram ◽

One Dimensional ◽

Stringed Instruments ◽

Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

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