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An Elementary Derivation of the Harmonic Oscillator Propagator  [PDF]
L. Moriconi
Physics , 2004, DOI: 10.1119/1.1715108
Abstract: The harmonic oscillator propagator is found straightforwardly from the free particle propagator, within the imaginary-time Feynman path integral formalism. The derivation presented here is extremely simple, requiring only elementary mathematical manipulations and no clever use of Hermite polynomials, annihilation & creation operators, cumbersome determinant evaluations or any kind of involved algebra.
The Zeta Function Method and the Harmonic Oscillator Propagator  [PDF]
F. A. Barone,C. Farina
Physics , 2005, DOI: 10.1119/1.1311784
Abstract: We show how the pre-exponential factor of the Feynman propagator for the harmonic oscillator can be computed by the generalized $\zeta$-function method. Besides, we establish a direct equivalence between this method and Schwinger's propertime method.


物理学报 , 2001,
Abstract: By means of canonical transformation,a direct quantization scheme is found for a harmonic oscillator whose damping coefficient is time-dependent.By adopting the Gaussian-type propagator and Feynman's path integral method,the exact wave function is derived.Some discussions made.
The possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator  [PDF]
J. Bohá\{v}cik,P. Pre\{v}snajder,P. August\'\{i}n
Physics , 2013,
Abstract: We find the possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator. We evaluate the conditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. We discuss the case, when the starting point of the propagator is zero. We present the results in analytical form for positive and negative frequency.
Reduction of superintegrable systems: the anisotropic harmonic oscillator  [PDF]
Miguel A. Rodriguez,Piergiulio Tempesta,Pavel Winternitz
Physics , 2008, DOI: 10.1103/PhysRevE.78.046608
Abstract: We introduce a new 2N--parametric family of maximally superintegrable systems in N dimensions, obtained as a reduction of an anisotropic harmonic oscillator in a 2N--dimensional configuration space. These systems possess closed bounded orbits and integrals of motion which are polynomial in the momenta. They generalize known examples of superintegrable models in the Euclidean plane.
Anisotropic harmonic oscillator in a static electromagnetic field  [PDF]
Qiong-Gui Lin
Physics , 2002,
Abstract: A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schr\"odinger equation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. In some of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherent and squeezed states and their time evolution are discussed in detail.


物理学报 , 1998,
Abstract: A damped harmonic oscillator was studied using canonical tramsformation and starting from the method of path integrals.An exact wavefunction for the damped harmonic oscillator has been obtained from a Gaussiantype propagator.The fluctuations of displacement and momentum at zero-point are also given.
Propagator for a time-dependent harmonic oscillator  [PDF]
John T. Whelan
Physics , 1997,
Abstract: This paper has been withdrawn, as the explicit form of the propagator can be found in: V.V.Dodonov, I.A.Malkin and V.I.Man'ko, J.Phys.A 8 (1975) L19 V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Int.J.Theor.Phys. 14 (1975) 37, Sec.3 V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Theor.Math.Phys. 24 (1975) 746, Sec.2 I am grateful to Professor Victor Dodonov for bringing this to my attention.
Generalized path-integral solution and coherent states of the harmonic oscillator in D-dimensions
Ma Yu-Quan,Zhang Jin,Chen Yong-Kang,Dai Hong,
,张 晋,陈永康,戴 宏

中国物理 B , 2005,
Abstract: We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time-dependent forced harmonic oscillator in D(D \ge 1) dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.
Symmetry Algebra of the Planar Anisotropic Quantum Harmonic Oscillator with Rational Ratio of Frequencies  [PDF]
Dennis Bonatsos,C. Daskaloyannis,P. Kolokotronis,D. Lenis
Physics , 1994,
Abstract: The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are determined using algebraic methods of general applicability to quantum superintegrable systems.
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