NEW TYPE SHIFT OPERATORS FOR THREE-DIMENSIONAL INFINITE WELL POTENTIAL

2011 ◽  
Vol 26 (05) ◽  
pp. 351-358 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Energy Spectrum ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Wave Functions ◽  
Shift Operators ◽  
New Type ◽  
Type Shift

New type shift operators for three-dimensional infinite well potential are identified to connect those quantum systems with different radials R but with the same energy spectrum. It should be pointed out that these shift operators depend on all variables contained in wave functions. Thus they establish a novel relation between wave functions ψlm(r) and ψ(l±1)(m±1)(r).

scholarly journals Modeling of circular quantum dots localized in double heterostructures

2021 ◽  
Vol 65 (1) ◽  
pp. 33-39
Author(s):  
V. V. Kudryashov ◽  
A. V. Baran
Keyword(s):  
Quantum Dots ◽  
Energy Spectrum ◽  
Energy Levels ◽  
Finite Depth ◽  
Wave Functions ◽  
Axially Symmetric ◽  
Confinement Potential ◽  
Double Heterostructures ◽  
New Type ◽  
Potential Parameters

The circular quantum dots localized in the double heterostructures are simulated by means of the axially symmetric smooth confinement potential of finite depth. For the proposed potential of new type, the exact wave functions and the energy levels of electron are found. The dependence of energy spectrum on potential parameters is investigated.

Exact solution of the relativistic finite-difference equation for the Coulomb plus a ring-shaped-like potential

2019 ◽  
Vol 34 (17) ◽  
pp. 1950089 ◽  
Author(s):  
Sh. M. Nagiyev ◽  
A. I. Ahmadov
Keyword(s):  
Energy Spectrum ◽  
Finite Difference ◽  
Jacobi Polynomials ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Dynamical Symmetry ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Radial Part ◽  
Radial Wave

In this paper, a three-dimensional problem of the motion of a charged relativistic particle in a noncentral Coulomb plus ring-shaped potential is studied. Our investigation is based on a finite-difference version of relativistic quantum mechanics. The energy eigenvalues and the corresponding wave functions are obtained analytically. It is shown that radial part and the angular part of the wave functions are expressed through the Meixner–Pollaczek polynomials and Jacobi polynomials, respectively. All relativistic expressions, for example, radial wave functions and energy spectrum, have the correct nonrelativistic limit. We also build a dynamical symmetry group for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.

scholarly journals Three-Dimensional Dirac Oscillator with Minimal Length: Novel Phenomena for Quantized Energy

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Malika Betrouche ◽  
Mustapha Maamache ◽  
Jeong Ryeol Choi
Keyword(s):  
Energy Spectrum ◽  
Energy Levels ◽  
Three Dimensional ◽  
Nonrelativistic Limit ◽  
Minimal Length ◽  
Wave Functions ◽  
Dirac Oscillator ◽  
Planck Length ◽  
Standard Case ◽  
Small Parameters

We study quantum features of the Dirac oscillator under the condition that the position and the momentum operators obey generalized commutationrelations that lead to the appearance of minimal length with the order of the Planck length,∆xmin=ℏ3β+β′, whereβandβ′are two positive small parameters. Wave functions of the system and the corresponding energy spectrum are derived rigorously. The presence of the minimal length accompanies a quadratic dependence of the energy spectrum on quantum numbern, implying the property of hard confinement of the system. It is shown that the infinite degeneracy of energy levels appearing in the usual Dirac oscillator is vanished by the presence of the minimal length so long asβ≠0. Not only in the nonrelativistic limit but also in the limit of the standard case(β=β′=0), our results reduce to well known usual ones.

New type shift operators for circular well potential in two dimensions

2010 ◽  
Vol 374 (40) ◽  
pp. 4112-4114 ◽  
Author(s):  
Guo-Hua Sun ◽  
Shi-Hai Dong
Keyword(s):  
Two Dimensions ◽  
Shift Operators ◽  
New Type ◽  
Type Shift

scholarly journals Effect of the Reynolds Number and Clearance Flow on the Aerodynamic Characteristics of a New Variable Inlet Guide Vane

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 172
Author(s):  
Hengtao Shi
Keyword(s):  
Reynolds Number ◽  
Guide Vane ◽  
Three Dimensional ◽  
High Growth ◽  
Aerodynamic Characteristics ◽  
Inlet Guide Vane ◽  
Separation Region ◽  
Clearance Flow ◽  
New Type ◽  
Variable Inlet Guide Vane

Recently, a new type of low-loss variable inlet guide vane (VIGV) was proposed for improving a compressor’s performance under off-design conditions. To provide more information for applications, this work investigated the effect of the Reynolds number and clearance flow on the aerodynamic characteristics of this new type of VIGV. The performance and flow field of two representative airfoils with different chord Reynolds numbers were studied with the widely used commercial software ANSYS CFX after validation was completed. Calculations indicate that, with the decrease in the Reynolds number Rec, the airfoil loss coefficient ω and deviation δ first increase slightly and then entered a high growth rate in a low range of Rec. Afterwards, a detailed boundary-layer analysis was conducted to reveal the flow mechanism for the airfoil performance degradation with a low Reynolds number. For the design point, it is the appearance and extension of the separation region on the rear portion; for the maximum incidence point, it is the increase in the length and height of the separation region on the former portion. The three-dimensional VIGV research confirms the Reynolds number effect on airfoils. Furthermore, the clearance leakage flow forms a strong stream-wise vortex by injection into the mainflow, resulting in a high total-pressure loss and under-turning in the endwall region, which shows the potential benefits of seal treatment.

scholarly journals Integrability, intertwiners and non-linear algebras in Calogero models

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francisca Carrillo-Morales ◽  
Francisco Correa ◽  
Olaf Lechtenfeld
Keyword(s):  
Wave Functions ◽  
Energy Eigenstates ◽  
Conserved Charges ◽  
Low Level ◽  
Shift Operators ◽  
Non Linear ◽  
Complete Sets

Abstract For the rational quantum Calogero systems of type A1⊕A2, AD3 and BC3, we explicitly present complete sets of independent conserved charges and their nonlinear algebras. Using intertwining (or shift) operators, we include the extra ‘odd’ charges appearing for integral couplings. Formulæ for the energy eigenstates are used to tabulate the low-level wave functions.

New Type of Two Degree of Freedom Motor Three-Dimensional Tooth Layer Field Application and Solution

2013 ◽  
Vol 391 ◽  
pp. 232-236
Author(s):  
Wen Huan Yang ◽  
Hai Xu Chen ◽  
Shuang Xie ◽  
Chun Ren Fang
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Field Application ◽  
Degree Of Freedom ◽  
Refined Method ◽  
New Type ◽  
Type Motor ◽  
Quasi Newton ◽  
Two Degree Of Freedom ◽  
Non Linear Equations

A new Multi-degree of freedom motor and its establishing of teeth layer parameters have been introduced in the paper, also including application method of database, namely using Quasi-Newton methods to solve the non-linear equations of the new motors magnetic circuit net, formed a refined method for designing and analyzing of motor. The establishment of 3d tooth layer parameters database, is provided for the calculation in the design of the new type motor conveniently.

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