Quantum mechanics of the inverted oscillator potential

The Color Glass Condensate (CGC) predicts the form of the nuclear wavefunction in QCD at very small x. Using this, we compute the wavefunction for the collision of two nuclei, infinitesimally in the forward light cone. We show that the Wigner transformation of this wavefunction generates rapidity dependent fluctuations around the boost invariant classical solution which describe the Glasma in the forward light cone.

show abstract

“…Let us consider a simple example [31]. Supposing that we have a convex parabolic potential as sketched in Fig.…”

Section: General Formulationmentioning

confidence: 99%

Initial singularity of the little bang

2007

View full text Add to dashboard Cite

show abstract

“…Despite these mathematical properties have been studied by several authors [18][19][20][21][22][23][24][25], a direct physical evidence of their implications is lacking, even in the simplest case of RHO. In this manuscript, we review the basics of TA-QM and of the GV approach to the RHO.…”

Section: Introductionmentioning

confidence: 99%

Irreversible evolution of a wave packet in the rigged-Hilbert-space quantum mechanics

Marcucci

Conti

2016

Phys. Rev. A

View full text Add to dashboard Cite

It is well known that a state with complex energy cannot be the eigenstate of a self-adjoint operator, as the Hamiltonian. Resonances, i.e. states with exponentially decaying observables, are not vectors belonging to the conventional Hilbert space. One can describe these resonances in an unusual mathematical formalism, based on the so-called Rigged Hilbert Space (RHS). In the RHS, the states with complex energy are denoted as Gamow Vectors (GV), and they model decay processes.We study GV of the Reversed Harmonic Oscillator (RHO), and we analytically and numerically investigate the unstable evolution of wave packets. We introduce the background function to study initial data not composed only by a summation of GV and we analyse different wave packets belonging to specific function spaces. Our work furnishes support to the idea that irreversible wave propagations can be investigated using Rigged Hilbert Space Quantum Mechanics and provides insights for the experimental investigation of irreversible dynamics.

show abstract

“…On the other hand, since their introduction quantum harmonic oscillators, both standard and inverted (repulsive) (cf. [11][12][13][14]), have proved to be one of the most useful models in particle physics. We analyse the effect of applying a uniform electromagnetic field to the energy levels of a quantum harmonic oscillator.…”

Section: Introductionmentioning

confidence: 99%

On Generalized Landau Levels

Krasoń

Milewski

2017

Acta Phys. Pol. A

View full text Add to dashboard Cite

We consider the dispersion of energy levels for both standard and inverted quantum harmonic oscillators in the presence of a uniform electromagnetic field. For this analysis we use a solution of the corresponding eigenproblem in terms of the Kummer functions. We find a complete description of the energy levels for a particle of mass m and electric charge q subject to the action of a harmonic oscillator and simultaneous uniform magnetic and electric fields. We also analyze the effect of spin on energy levels for an electron.

show abstract

Quantum mechanics of the inverted oscillator potential

Cited by 228 publications

References 17 publications

Initial singularity of the little bang

Initial singularity of the little bang

Irreversible evolution of a wave packet in the rigged-Hilbert-space quantum mechanics

On Generalized Landau Levels

Contact Info

Product

Resources

About