A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass and imaginary frequency. The latter may be reduced to an ordinary harmonic oscillator by means of another unitary (canonical) transformation. A simple analysis...

By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the qoscillator are obtained. They satisfy a q-oscillator algebra as a consequence of the shape-invariance of the Hamiltonian. A second set of q-oscillator is derived from the exact Heisenberg operator solution. Now the q-oscillator stands on th...

We propose a new type of three-cluster equation which uses two-cluster resonating-groupmethod (RGM) kernels. In this equation, the orthogonality of the total wave-function to two-cluster Pauli-forbidden states is essential to eliminate redundant components admixed in the three-cluster systems. The explicit energy-dependence inherent in the exchange RGM kernel is self-consistently determined. Fo...

We assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the Dirac matrices. Then by making use of a suitable ansatz, the Dirac equation has a very simple solution which is exact. We then have calculated the static properties of the nucleon in the ...

We consider a radiation from a uniformly accelerating harmonic oscillator whose minimal coupling to the scalar field changes suddenly. The exact time evolutions of the quantum operators are given in terms of a classical solution of a forced harmonic oscillator. After the jumping of the coupling constant there occurs a fast absorption of energy into the oscillator, and then a slow emission follo...

Lie-isotopic lifting of the commutation and anticommutation relations of creation-annihilation bosonic and fermionic operators is considered. Lie-isotopic generalization of the associated supersymmetry generators and of the underlying superalgebra in considering of the Lie-isotopically lifted hamiltonian of supersymmetric quantum mechanical oscillator is defined. The generalised oscillator has ...

In this paper we revisit the quantum damped harmonic oscillator and construct an interesting approximate solution in the operator algebra level. Namely, we first give the general solution to the Lindblad form (equation) and next construct an approximate solution to the full equation by use of it. Our method is a milestone to construct the general solution. In this paper we revisit dynamics of a...

Let Jσ be the Dunkl harmonic oscillator on R (σ > −1/2). For 0 < u < 1 and ξ > 0, it is proved that, if σ > u − 1/2, then the operator U = Jσ + ξ|x|−2u, with appropriate domain, is essentially self-adjoint in L(R, |x|dx), the Schwartz space S is a core of U 1/2 , and U has a discrete spectrum, which is estimated in terms of the spectrum of Jσ. A generalization Jσ,τ of Jσ is also considered by t...

We consider the perturbed harmonic oscillator TDψ = −ψ′′ + x2ψ + q(x)ψ, ψ(0) = 0 in L(R+), where q ∈ H+ = {q′, xq ∈ L(R+)} is a real-valued potential. We prove that the mapping q 7→ spectral data = {eigenvalues of TD} ⊕ {norming constants} is one-to-one and onto. The complete characterization of the set of spectral data which corresponds to q ∈ H+ is given. Moreover, we solve the similar invers...

In present work we consider C∗-algebras C∗(Af ) associated with simple unimodal nonbijective dynamical system (f,R) with special requirements. In the case when f is polynomial, Af = C〈X,X∗| XX∗ = f(X∗X)〉 and C∗(Af ) is its enveloping C∗-algebra. As typical examples we consider one-parameter family fμ(x) = μx(1 − x) and two-parameter family called Unharmonic Quantum Oscillator fp,q(x) = 1+ px− q...