Bosons and fermions in a one-dimensional harmonic oscillator potential

2002 ◽  
Vol 90 (3) ◽  
pp. 1249-1252
Author(s):  
Brian G. Wybourne
Keyword(s):  
Harmonic Oscillator ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
One Dimensional

scholarly journals Exact Solutions of the Mass-Dependent Klein-Gordon Equation with the Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Bahar ◽  
F. Yasuk
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Oscillator Potential ◽  
Ansatz Method ◽  
Harmonic Oscillator Potential ◽  
Klein Gordon ◽  
Dependent Mass ◽  
Mass Dependent ◽  
Klein Gordon Equation

Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

GROUND STATE OF N HARMONICALLY BOUND ANYONS IN A MAGNETIC FIELD

1992 ◽  
Vol 07 (38) ◽  
pp. 3593-3600
Author(s):  
R. CHITRA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Harmonic Oscillator ◽  
Ground State ◽  
Harmonic Frequency ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Thomas Fermi ◽  
Large N ◽  
The Magnetic Field

The properties of the ground state of N anyons in an external magnetic field and a harmonic oscillator potential are computed in the large-N limit using the Thomas-Fermi approximation. The number of level crossings in the ground state as a function of the harmonic frequency, the strength and the direction of the magnetic field and N are also studied.

scholarly journals NEW FEATURES IN SUPERSYMMETRY BREAKDOWN IN QUANTUM MECHANICS

1996 ◽  
Vol 11 (19) ◽  
pp. 1563-1567 ◽  
Author(s):  
BORIS F. SAMSONOV
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Mechanical Model ◽  
State Energy ◽  
Vacuum State ◽  
Quantum Mechanical ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Quantum Mechanical Model ◽  
Higher Derivative

The supersymmetric quantum mechanical model based on higher-derivative supercharge operators possessing unbroken supersymmetry and discrete energies below the vacuum state energy is described. As an example harmonic oscillator potential is considered.

scholarly journals Static and Dynamic Properties of a Few Spin 1/2 Interacting Fermions Trapped in a Harmonic Potential

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1196
Author(s):  
Abel Rojo-Francàs ◽  
Artur Polls ◽  
Bruno Juliá-Díaz
Keyword(s):  
Sum Rules ◽  
Dynamic Properties ◽  
Interaction Strength ◽  
Dynamical Structure ◽  
Static Properties ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
One Dimensional ◽  
State Densities ◽  
Analytical Expressions

We provide a detailed study of the properties of a few interacting spin 1 / 2 fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of direct diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime. The N = 2 case is used to benchmark our numerical techniques with the known exact solution of the problem. After a detailed description of the numerical methods, in a tutorial-like manner, we present the static properties of the system for N = 2 , 3 , 4 and 5 particles, e.g., low-energy spectrum, one-body density matrix, ground-state densities. Then, we consider dynamical properties of the system exploring first the excitation of the breathing mode, using the dynamical structure function and corresponding sum-rules, and then a sudden quench of the interaction strength.

Sign in / Sign up

Export Citation Format

Share Document