scholarly journals A family of analytically solvable Schrödinger equations related by Levi-Civita transformation

2019 ◽  
Vol 16 (3) ◽  
pp. 103
Author(s):  
Le Dai Nam ◽  
Phan Anh Luan ◽  
Luu Phong Su ◽  
Phan Ngoc Hung
Keyword(s):  
Exact Solution ◽  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Anharmonic Oscillator ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Schrödinger Equations ◽  
Two Dimensional ◽  
Spatial Transformations ◽  
Solvable Problems

Some two-dimensional problems in non-relativistic quantum mechanics can connect to each other by certain spatial transformations such as Levi-Civita transformation. This property allows forming a series of two-dimensional problems into an interrelated family. Starting from two related problems namely Coulomb plus harmonic oscillator and sextic double-well anharmonic oscillator potentials, such family is constructed via repeatedly applying Levi-Civita transformations. Obviously, this family contains various of exactly analytically solvable problems. The quasi-exact solution for each unknown member of this family is also obtained and systematically investigated.

GAUGE INVARIANCE IN NON-RELATIVISTIC MANY-BODY THEORY

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2201-2208 ◽  
Author(s):  
J. FRÖHLICH ◽  
U.M. STUDER
Keyword(s):  
Quantum Mechanics ◽  
Gauge Invariance ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Spin Liquids ◽  
Many Body ◽  
Many Body Theory ◽  
Hall Effects ◽  
Body Theory

We review some recent results on the physics of two-dimensional, incompressible electron and spin liquids. These results follow from Ward identities reflecting the U(1) em × SU(2) spin -gauge invariance of non-relativistic quantum mechanics. They describe a variety of generalized quantized Hall effects.

Statistical properties of the q-deformed relativistic Dirac oscillator in minimal length quantum mechanics

2018 ◽  
Vol 96 (1) ◽  
pp. 25-29 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W.S. Chung
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
External Magnetic Field ◽  
Relativistic Quantum ◽  
Two Dimensions ◽  
Minimal Length ◽  
Statistical Properties ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Dirac Oscillator

In this article, we introduce a two-dimensional Dirac oscillator in the presence of an external magnetic field in terms of q-deformed creation and annihilation operators in the framework of relativistic quantum mechanics with minimal length. We discuss the eigenvalues of q-deformed Dirac oscillator in two dimensions and report the statistical quantities of the system for a small real q.

scholarly journals Exact Solutions of the (2+1)-Dimensional Dirac Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Non-commutative Phase Space

2015 ◽  
Vol 70 (8) ◽  
pp. 619-627 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Phase Space ◽  
Hypergeometric Functions ◽  
Relativistic Quantum ◽  
Minimal Length ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Dirac Oscillator

AbstractWe consider a two-dimensional Dirac oscillator in the presence of a magnetic field in non-commutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl–Teller potential. The eigenvalues are found, and the corresponding wave functions are calculated in terms of hypergeometric functions.

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