scholarly journals A COHERENT STATE PATH INTEGRAL FOR ANYONS

1995 ◽  
Vol 10 (12) ◽  
pp. 985-989 ◽  
Author(s):  
J. GRUNDBERG ◽  
T.H. HANSSON
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Coherent States ◽  
Integral Formula ◽  
Harmonic Potential ◽  
One Dimensional ◽  
Change Of Variables ◽  
The One ◽  
State Path

We derive an su (1, 1) coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to an su (1, 1) version of the Holstein-Primakoff transformation.

scholarly journals SU(2) COHERENT STATE PATH INTEGRALS LABELED BY A FULL SET OF EULER ANGLES: BASIC FORMULATION

2012 ◽  
Vol 26 (29) ◽  
pp. 1250143 ◽  
Author(s):  
MASAO MATSUMOTO
Keyword(s):  
Integral Representation ◽  
Coherent State ◽  
Path Integral ◽  
Coherent States ◽  
Path Integrals ◽  
Euler Angles ◽  
Geometric Phases ◽  
Path Integral Representation ◽  
General Systems ◽  
State Path

We develop a basic formulation of the spin (SU(2)) coherent state path integrals based not on the conventional highest or lowest weight vectors but on arbitrary fiducial vectors. The coherent states, being defined on a 3-sphere, are specified by a full set of Euler angles. They are generally considered as states without classical analogues. The overcompleteness relation holds for the states, by which we obtain the time evolution of general systems in terms of the path integral representation; the resultant Lagrangian in the action has a monopole-type term à la Balachandran et al. as well as some additional terms, both of which depend on fiducial vectors in a simple way. The process of the discrete path integrals to the continuous ones is clarified. Complex variable forms of the states and path integrals are also obtained. During the course of all steps, we emphasize the analogies and correspondences to the general canonical coherent states and path integrals that we proposed some time ago. In this paper we concentrate on the basic formulation. The physical applications as well as criteria in choosing fiducial vectors for real Lagrangians, in relation to fictitious monopoles and geometric phases, will be treated in subsequent papers separately.

Eigenvalues of the Potential Function V=z4±Bz2 and the Effect of Sixth Power Terms

1970 ◽  
Vol 24 (1) ◽  
pp. 73-80 ◽  
Author(s):  
Jaan Laane
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Potential Function ◽  
Schrodinger Equation ◽  
Harmonic Potential ◽  
Reduced Form ◽  
Approximation Formula ◽  
One Dimensional ◽  
Ring Puckering ◽  
The One

The one-dimensional Schrödinger equation in reduced form is solved for the potential function V = z4+ Bz2 where B may be positive or negative. The first 17 eigenvalues are reported for 58 values of B in the range −50⩽ B⩽100. The interval of B between the tabulated values is sufficiently small so that the eigenvalues for any B in this range can be found by interpolation. At the limits of the range of B the potential function approaches that of a harmonic oscillator with only small anharmonicity. The effect of a small Cz6 term on this potential is studied and it is concluded that a previously reported approximation formula is quite applicable but only for positive values of B. The success of the quartic—harmonic potential function for the analysis of the ring-puckering vibration is shown; it is also demonstrated that the same potential serves as a useful approximation for many other systems, especially those of the double minimum type.

EXACT SOLUTIONS, LADDER OPERATORS AND BARUT–GIRARDELLO COHERENT STATES FOR A HARMONIC OSCILLATOR PLUS AN INVERSE SQUARE POTENTIAL

2005 ◽  
Vol 19 (28) ◽  
pp. 4219-4227 ◽  
Author(s):  
SHI-HAI DONG ◽  
M. LOZADA-CASSOU
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Coherent States ◽  
Factorization Method ◽  
Ladder Operators ◽  
Dynamical Group ◽  
One Dimensional ◽  
Hidden Symmetry ◽  
The One ◽  
Analytical Expressions

We present exact solutions of the one-dimensional Schrödinger equation with a harmonic oscillator plus an inverse square potential. The ladder operators are constructed by the factorization method. We find that these operators satisfy the commutation relations of the generators of the dynamical group SU(1, 1). Based on those ladder operators, we obtain the analytical expressions of matrix elements for some related functions ρ and [Formula: see text] with ρ=x2. Finally, we make some comments on the Barut–Girardello coherent states and the hidden symmetry between E(x) and E(ix) by substituting x→ix.

scholarly journals Feynman Path Integral in Multiple-Slit and its Simulation

2019 ◽  
Vol 2 (1) ◽  
pp. 63-70
Author(s):  
Mahendra Satria Hadiningrat
Keyword(s):  
Interference Pattern ◽  
Path Integral ◽  
Electron Distribution ◽  
Analytic Solution ◽  
Integral Formula ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
One Dimensional ◽  
The One ◽  
Theoretical Results

In this article we hold on an analytic solution of the well-known cases of difraction and interference of electrons through one and two slits (simply that, the one-dimensional case is assumed only). In addition, we hold an approximations of the electron distribution which offer the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could also serve an awesome introduction to multiple slits interference. Then it is comparing between theoretical results and simulation in order to get interference pattern of it.

PERELOMOV AND BARUT–GIRARDELLO SU(1, 1) COHERENT STATES FOR HARMONIC OSCILLATOR IN ONE-DIMENSIONAL HALF SPACE

2006 ◽  
Vol 21 (12) ◽  
pp. 2635-2644 ◽  
Author(s):  
Q. H. LIU ◽  
H. ZHUO
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Half Space ◽  
Ground State ◽  
Classical Limit ◽  
Coherent States ◽  
Mean Values ◽  
One Dimensional ◽  
The Mean

The Perelomov and the Barut–Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below [Formula: see text] that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut–Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.

PERIODIC COHERENT STATES AND A PATH INTEGRAL FOR SPINS

1990 ◽  
Vol 05 (02) ◽  
pp. 375-390 ◽  
Author(s):  
TARO KASHIWA
Keyword(s):  
Coherent State ◽  
Path Integral ◽  
Coherent States ◽  
Integral Formula ◽  
Integral Formalism ◽  
Path Integral Formalism ◽  
Quantum Spins

A path integral formalism for quantum spins is discussed with the aid of a new coherent state. Under the study, we can see the reason why the path integral formula proposed recently by Nielsen and Rohrlich works so well and the origin of the parameter in their formula. A generalization to the case where spin magnitude is unfixed is also presented.

scholarly journals On The Information-Theoretical Entropy for Some Quantum Oscillators

2013 ◽  
Vol 57 (1) ◽  
pp. 67-79
Author(s):  
Dušan Popov ◽  
Nicolina Pop ◽  
Simona Șimon
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Wehrl Entropy ◽  
One Dimensional ◽  
The One ◽  
Classical Entropy ◽  
Thermal States

Abstract The information-theoretical entropy, also called the “classical” entropy, was introduced by Wehrl in terms of the Glauber coherent states (CSs) | z > , i.e. the CSs corresponding to the one-dimensional harmonic oscillator (HO-1D). In the present paper, we have focused our attention on the examination of the information-theoretical entropy, i.e. the Wehrl entropy, for both the pure and the mixed (thermal) states of some quantum oscillators.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

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