Energy level distributions and chaos in quantum mechanics

1985 ◽  
pp. 86-107 ◽  
Author(s):  
Giulio Casati
Keyword(s):  
Quantum Mechanics ◽  
Energy Level

INVARIANT EIGEN-OPERATOR METHOD OF DERIVING ENERGY-LEVEL GAP FOR NONCOMMUTATIVE QUANTUM MECHANICS

2005 ◽  
Vol 20 (09) ◽  
pp. 691-698 ◽  
Author(s):  
SI-CONG JING ◽  
HONG-YI FAN
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Operator Method ◽  
Simple Algebra ◽  
New Method ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Quantum

We propose a new method to derive energy-level gap for Hamiltonians in the context of noncommutative quantum mechanics (NCQM). This method relies on finding invariant eigen-operators whose commutators with Hamiltonian are still the operators themselves but with some eigenvalue-like coefficients, which correspond to the energy-level gaps of the systems. Based on this method, only after some simple algebra, we derive the energy-level gaps for several important systems in NCQM, and most of these results have not been reported in literature so far.

Quantum mechanics on (anti)-de Sitter background II: Ramsauer–Townsend effect and WKB method

2018 ◽  
Vol 33 (26) ◽  
pp. 1850150 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Harmonic Oscillator ◽  
Wkb Method ◽  
De Sitter ◽  
Quantum Harmonic Oscillator ◽  
One Dimensional ◽  
Sitter Background ◽  
The One

Based on the one-dimensional quantum mechanics on (anti)-de Sitter background [W. S. Chung and H. Hassanabadi, Mod. Phys. Lett. A 32, 26 (2107)], we discuss the Ramsauer–Townsend effect. We also formulate the WKB method for the quantum mechanics on (anti)-de Sitter background to discuss the energy level of the quantum harmonic oscillator and quantum bouncer.

Energy Level Width of 2DEG in Different Well in Mesoscopic System

2013 ◽  
Vol 706-708 ◽  
pp. 395-398
Author(s):  
Gang Xu ◽  
Ye Lu He
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Quantum Number ◽  
Field Intensity ◽  
Uncertainty Relation ◽  
Electron Gas ◽  
Energy Width ◽  
Level Width ◽  
Classical Particles ◽  
Electronic Field

Applying theories on quasi-classical particles and the uncertainty relation of quantum mechanics, we get the formula of uncertainty and energy level width in triangular well and parabolic well of two dimension electron gas (2DEG).Based on these ,we find energy width will increase along with the increasing of electronic field intensity and quantum number at the same electronic field, the energy width of parabolic well is more narrow than width of triangular well. At the same time, the result of this paper is agreement with the experiment.

On the missing anisotropic space inside atoms in quantum mechanics

2021 ◽  
Vol 34 (3) ◽  
pp. 351-365
Author(s):  
W. Guglinski
Keyword(s):  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
Energy Level ◽  
Electron Motion ◽  
Anisotropic Space ◽  
Successful Result ◽  
The Real ◽  
Experimental Values ◽  
Schrödinger's Equation ◽  
Fundamentals Of Quantum Mechanics

Schrödinger developed his famous equation from the standard wavelength. However, as demonstrated here, inside the atom, the electron does not move according to de Broglie-Einstein’s postulate λ = h/p, because the wavelength of the electron’s motion varies with the distance to the nucleus. Therefore, Schrödinger’s equation does not quantify the real electron’s motion in atoms. Here, the equation of a variable wavelength for electron motion inside atoms is introduced. The calculation, applied to the hydrogen atom, achieves energy level values very close to the experimental values. This successful result can provide a deeper understanding of the behavior of electrons in atoms and improve the fundamentals of quantum mechanics (QM). However, beyond the question concerning the postulate λ = h/p, two other fundamental principles may be missing in modern QM, and they are: an anisotropic space inside atoms and a motion of the electron through a helical trajectory.

Study on Energy Materials with Energy Level Width of 2DEG in Triangular Well

2013 ◽  
Vol 327 ◽  
pp. 342-345
Author(s):  
Gang Xu ◽  
Yue Sun
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Ground State ◽  
Uncertainty Relation ◽  
Electron Gas ◽  
Energy Materials ◽  
Energy Width ◽  
Level Width ◽  
Classical Particles ◽  
Electronic Field

Applying theories on quasi-classical particles and the uncertainty relation of quantum mechanics, we deduce the formula of energy uncertainty in energy materials with electric field .We use it to two dimension electron gas (2DEG) in triangular well and get its energy width. Based on these, we find energy width will increase along with the increasing of electronic field intensity. At the same time, the energy width of the first excitated state is wider than the ground state, At the same time, the result of this paper is agreement with the experiment.

Energy level crossings in quantum mechanics

1988 ◽  
Vol 1 (2) ◽  
pp. 147-162 ◽  
Author(s):  
W. H. Steeb ◽  
A. J. van Tonder ◽  
C. M. Villet ◽  
S. J. M. Brits
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Level Crossings
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