THE PATH INTEGRAL APPROACH TO AN N-PARTICLE IN A PT-SYMMETRIC HARMONIC OSCILLATOR

2010 ◽  
Vol 24 (28) ◽  
pp. 5579-5587
Author(s):  
SIKARIN YOO-KONG
Keyword(s):  
Harmonic Oscillator ◽  
Total Energy ◽  
Path Integral ◽  
Path Integrals ◽  
Harmonic Potential ◽  
Integral Approach ◽  
Path Integral Approach ◽  
System Of Particles

We study a path integral approach to a system of particles in a PT-symmetric harmonic potential: V(x)=mω2(x2±2iεx)/2. The eigenvalues and eigenstates of the system have been calculated. We find that the total energy of the system is real. The connection between the non-Hermitian and Hermitian Hamiltonians has been discussed and we also establish this connection in the context of path integrals via a considering model.

ENERGY-DEPENDENT POTENTIAL AND NORMALIZATION OF WAVE FUNCTION

2013 ◽  
Vol 28 (18) ◽  
pp. 1350079 ◽  
Author(s):  
A. BENCHIKHA ◽  
L. CHETOUANI
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Spectral Decomposition ◽  
Wave Functions ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Dependent Potential ◽  
Energy Dependent

The problem of normalization related to energy-dependent potentials is examined in the context of the path integral approach, and a justification is given. As examples, the harmonic oscillator and the hydrogen atom (radial) where, respectively the frequency and the Coulomb's constant depend on energy, are considered and their propagators determined. From their spectral decomposition, we have found that the wave functions extracted are correctly normalized.

Energy-dependent harmonic oscillator in noncommutative space: A path integral approach

2017 ◽  
Vol 32 (32) ◽  
pp. 1750194 ◽  
Author(s):  
A. Benchikha ◽  
M. Merad
Keyword(s):  
Harmonic Oscillator ◽  
Path Integral ◽  
Wave Functions ◽  
Polar Coordinates ◽  
Integral Approach ◽  
Noncommutative Space ◽  
Energy Eigenvalues ◽  
Path Integral Approach ◽  
Noncommutative Quantum Mechanics ◽  
Energy Dependent

In the context of noncommutative quantum mechanics, the energy-dependent harmonic oscillator problem is solved via path integral approach. The propagator of the system is calculated using polar coordinates. The normalized wave functions and the energy eigenvalues are obtained in two different cases.

PATH INTEGRAL QUANTIZATION OF THE CHIRAL SCHWINGER MODEL IN BOSONIZED FORM

2008 ◽  
Vol 23 (27n28) ◽  
pp. 4517-4532 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Path Integral ◽  
Gauge Invariance ◽  
Path Integrals ◽  
Integral Approach ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Path Integral Quantization ◽  
Path Integral Approach ◽  
Physical Quantities

The development of the Wess–Zumino action or one-cycle is reviewed from the path integral approach. This is related to the occurrence of anomalies in the theory, and generally signifies a breakdown of gauge invariance. The Jackiw–Rajaraman version of the chiral Schwinger model is studied by means of path integrals. It is shown how the model can be made gauge invariant by using a Wess–Zumino term to write a gauge invariant Lagrangian. The model is considered only in bosonized form without any reference to fermions. The constraints are determined. These components are then used to write a path integral quantization for the bosonized form of the model. Some physical quantities and information, in particular, propagators are derived from the path integral.

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