The generalized invariant and its eigenstates of a general quadratic oscillator are found. The Schrödinger wave functions for the eigenstates are also found in analytically closed forms. The conditions for the existence of the cyclic initial state (CIS) are studied and the corresponding nonadiabatic Berry phase is calculated explicitly. 03.65.-w Typeset using REVTEX ∗e-mail:[email protected]...

The energy-momentum relations for massive and massless particles are E = p/2m and E = pc respectively. According to Einstein, these two different expressions come from the same formula E = √ (cp) + mc. Quarks and partons are believed to be the same particles, but they have quite different properties. Are they two different manifestations of the same covariant entity as in the case of Einstein’s...

We find that the energy spectra of four and five anyons in a harmonic potential exhibit some mirror symmetric (reflection symmetric about the semionic statistics point θ = π/2) features analogous to the mirror symmetry in the two and three anyon spectra. However, since the l = 0 sector remains non-mirror symmetric, the fourth and fifth virial coeffients do not reflect this symmetry. 03.65.Ge, 0...

I describe harmonic-oscillator-based effective theory (HOBET) and explore the extent to which the effects of excluded higher-energy oscillator shells can be represented by a contact-gradient expansion in next-to-next-to-leading order (NNLO). I find the expansion can be very successful provided the energy dependence of the effective interaction, connected with missing long-wavelength physics ass...

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigrou...

The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension. Finally the map of Schödinger equation from noncommutative space to commutative space is obtained. PACS number: 03.65Bz, 11.90.+t

An analytic resolution of the covariant oscillator quark model for baryons is presented. Our harmonic potential is a general quadratic potential which can simulate both a ∆-shaped configuration or a simplified Y configuration where the junction is located at the centre of mass. The addition of new terms simulating the one gluon exchange process and the quark self-energy is discussed, and a comp...

By a conservation law we mean a quantity constructed from the coordinates, velocities, accelerations, etc. of the system that does not change as the system evolves in time. When the equations of motion are second order, conservation laws typically arise as functions on the velocity phase (possibly with explicit time dependence). Conservation of energy, momentum and angular momentum are familiar...

We perform an analytical study of the correspondence between a classical oscillator with frequency perturbed by a coloured noise and the one-dimensional Anderson-type model with correlated diagonal disorder. It is rigorously shown that localisation of electronic states in the quantum model corresponds to exponential divergence of nearby trajectories of the classical random oscillator. We discus...

The method of effective interaction, traditionally used in the framework of an harmonic oscillator basis, is applied to the hyperspherical formalism of few–body nuclei (A = 3 ÷ 6). The separation of the hyperradial part leads to a state dependent effective potential. Undesirable features of the harmonic oscillator approach associated with the introduction of a spurious confining potential are a...