Invariant Schrodinger Equation Research Articles

Schrodinger Maps and their Associated Frame Systems

In this paper we establish the equivalence of solutions bet ween Schrodinger maps intoS 2 orH 2 and their associated gauge invariant Schrodinger equations. We also establish the existence of global weak solutions intoH 2 in two space dimensions. We extend these ideas for maps into compact hermitian symmetric manifolds with trivial first cohomology.

On the local smoothing for a class of conformally invariant Schrodinger equations

We present some a priori bounds from above and from below for solutions to a class of conformally invariant Schrodinger equations. As a by-product we deduce some new uniqueness results.

Suq(2)-invariant Schrödinger equation of the three-dimensional harmonic oscillator

We propose a q-deformation of the \( \mathfrak{s}\mathfrak{u}\left( 2 \right) \)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but also to calculate the expectation values of some physically-relevant operators. Here we consider the case of the isotropic harmonic oscillator and of the quadrupole operator governing its interaction with an external field. We obtain the spectrum and wave functions both for \( q \in \mathbb{R}^ + \) and generic \( q \in S^i \), and study the effects of the q-value range and of the arbitrariness in the \( \mathfrak{s}\mathfrak{u}_\mathfrak{q} \left( 2 \right) \) Casimir operator choice. We then show that the quadrupole operator in l=0 states provides a good measure of the deformation influence on the wave functions and on the Hilbert space spanned by them.

Su q (2)-invariant Schrödinger equations

We set upsu q (2)-invariant Schrodinger equations within the usual framework of quantum mechanics. We show that the stationary equations reduce to radial ordinary differential equations by using the q-Spherical Harmonics. We apply these results to deformations of the free particle and of the hydrogen atom, for which we explicitly solve the equations and compare the deformed and undeformed theories.

Schr�dinger equations for su q (2)-invariant quantum systems

By deforming the Hamiltonian of a spinless particle in a central potential we set up suq(2)-invariant Schrodinger equations within the usual framework of quantum mechanics. Different deformations correspond to a given Hamiltonian. We explicitly solve different stationary Schrodinger equations for the free particle and for the hydrogen atom, and compare the associated energy spectra.

Free particle in q-deformed configuration space

The SO q (N)-invariant Schrodinger equation for the free particle is formulated in polar coordinates as a partial differential equation in noncommutative geometry. For each value of the total angular momentum, a Hilbert space of radial functions is constructed as the space of normalizable functions respective to the q-integral. The spectrum of the Hamiltonian is found to be discrete.