Accurate and fully analytical expressions for quantum energy levels in finite potential wells for nanoelectronic compact modeling

2021 ◽  
Author(s):  
Daniel R. Celino ◽  
Murilo A. Romero ◽  
Regiane Ragi
Keyword(s):  
Energy Levels ◽  
Compact Modeling ◽  
Potential Wells ◽  
Quantum Energy ◽  
Analytical Expressions

QUANTUM EFFECTS OF A DOMAIN WALL IN THE FERROMAGNETIC SYSTEM

2011 ◽  
Vol 25 (06) ◽  
pp. 413-418
Author(s):  
JI-SUO WANG ◽  
KE-ZHU YAN ◽  
BAO-LONG LIANG
Keyword(s):  
Domain Wall ◽  
Unitary Transformation ◽  
Energy Levels ◽  
Canonical Quantization ◽  
Classical Equation ◽  
Quantization Method ◽  
Damping Term ◽  
Quantum Energy ◽  
Moving Wall ◽  
Ferromagnetic System

Starting from the classical equation of the motion of a domain wall in the ferromagnetic systems, the quantum energy levels of the wall and the corresponding eigenfunctions in the case of considering damping term are given by using the canonical quantization method and unitary transformation. The quantum fluctuations of displacement and momentum of the moving wall has also been given as well as the uncertain relation.

Analytical solution of the Shredinger equation for the linear combination of the Manning-Rosen and the class of Yukawa potential

2021 ◽  
pp. 157-169
Author(s):  
G.A. Bayramova ◽  
Keyword(s):  
Analytical Solution ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Radial Wave ◽  
Rosen Potential ◽  
Analytical Expressions ◽  
Potential Parameters

In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning-Rosen potential plus the Yukawa class. To overcome the difficulties arising in the case l ≠ 0 in the centrifugal part of the Manning-Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. And also obtained eigenfunctions expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.

Energy spectrum and wavefunction of electrons in hybrid superconducting nanowires

2016 ◽  
Vol 30 (13) ◽  
pp. 1642008 ◽  
Author(s):  
S. P. Kruchinin
Keyword(s):  
Energy Spectrum ◽  
Energy Levels ◽  
Superconducting Nanowires ◽  
Quantum Energy ◽  
Close Proximity ◽  
Superconducting Nanowire

Recent experiments have fabricated structured arrays. We study hybrid nanowires, in which normal and superconducting regions are in close proximity, by using the Bogoliubov–de Gennes equations for superconductivity in a cylindrical nanowire. We succeed to obtain the quantum energy levels and wavefunctions of a superconducting nanowire. The obtained spectra of electrons remind Hofstadter’s butterfly.

Calculation of spectral determinants

1994 ◽  
Vol 447 (1930) ◽  
pp. 413-437 ◽  
Keyword(s):  
Periodic Orbit ◽  
Finite Number ◽  
Dirichlet Series ◽  
Energy Levels ◽  
Euler Product ◽  
Quantum Energy ◽  
Type Formula

A method for regularizing spectral determinants is developed which facilitates their computation from a finite number of eigenvalues. This is used to calcu­late the determinant ∆ for the hyperbola billiard over a range which includes 46 quantum energy levels. The result is compared with semiclassical periodic orbit evaluations of ∆ using the Dirichlet series, Euler product, and a Riemann-Siegel-type formula. It is found that the Riemann-Siegel-type expansion, which uses the least number of orbits, gives the closest approximation. This provides explicit numerical support for recent conjectures concerning the analytic proper­ties of semiclassical formulae, and in particular for the existence of resummation relations connecting long and short pseudo-orbits.

Lower bounds for quantum energy levels through statistical mechanics methods

1980 ◽  
Vol 21 (4) ◽  
pp. 834-839 ◽  
Author(s):  
L. Nitti ◽  
M. Pellicoro ◽  
M. Villani
Keyword(s):  
Statistical Mechanics ◽  
Lower Bounds ◽  
Energy Levels ◽  
Quantum Energy

Quantum states in a nanotube quantum dot

2017 ◽  
Vol 31 (25) ◽  
pp. 1745023
Author(s):  
J. T. Wang ◽  
J. D. Fan
Keyword(s):  
Carbon Nanotube ◽  
High Efficiency ◽  
Energy Levels ◽  
Quantum States ◽  
Semiconductor Surface ◽  
Energy Structure ◽  
Two Dimensional ◽  
Quantum Energy ◽  
Quantum Bit ◽  
Computer Chips

In this paper, we carry out a theoretical calculation of quantum state and quantum energy structure in carbon nanotube embedded semiconductor surface. In this theoretical model, the electrons in the carbon nanotube are considered as in a two-dimensional cylindrical surface. Their motion, therefore, can be described by the Dirac equation. We solve the equation and find that the energy levels are quantized and are linearly dependent on the wave vectors along the [Formula: see text]-direction that is along the direction of the nanotube. This type of energy structure may have potential application for fabricating high efficiency solar cell or quantum bit in computer chips.

Sweep rate effects and quantum energy levels in Josephson junctions

1990 ◽  
Vol 165-166 ◽  
pp. 947-948
Author(s):  
Paolo Silvestrini ◽  
Luigi Frunzio ◽  
Roberto Cristiano
Keyword(s):  
Josephson Junctions ◽  
Energy Levels ◽  
Sweep Rate ◽  
Quantum Energy ◽  
Rate Effects

The influence of classical resonances on quantum energy levels

1993 ◽  
Vol 99 (5) ◽  
pp. 3659-3668 ◽  
Author(s):  
B. Ramachandran ◽  
Kenneth G. Kay
Keyword(s):  
Energy Levels ◽  
Quantum Energy

The Zero-Point Oscillations in the Planck Vacuum State and Its Coordinate Uncertainty

2021 ◽  
Vol 6 (4) ◽  
pp. 13-15
Author(s):  
William C. Daywitt
Keyword(s):  
First Principles ◽  
Energy Levels ◽  
Zero Point ◽  
Vacuum State ◽  
Short Paper ◽  
Quantum Energy

This short paper argues that the charged quantum oscillators in the quasi-continuum Planck vacuum (PV) state are responsible for the zero-point oscillations in that state. The Planck particle (PP) quantum energy levels for the oscillators are derived from first principles. The PV coordinate uncertainty concerning the PV structure easily follows from these results.

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