Abstract

We study the Schrodinger-Newton equations proposed by Penrose to describe his view that quantum state reduction occurs due to some gravitational e?ffect. They consist of a system of equations obtained by coupling together the linear Schrodinger equation of quantum mechanics with the Poisson equation from Newtonian mechanics. We assume that the magnetic vector potential A and the electric potential V in the linear Schrodinger equation are compatible with the action of a group G of linear isometries of R^3. Then, for any given homomorphism ? $ au$ on G into the unit complex numbers, we show that there is a combined e?ffect of the symmetries and the potential V on the number of semiclassical solutions u which satisfy $u(gx) = au?(g)u(x)$ for all $g in G, x in R3$. We also study the concentration behavior of these solutions in the semiclassical limit.

Autore Pugliese

• Cingolani Silvia

Tutti gli autori

• CINGOLANI S , CLAPP M , SECCHI S

Titolo volume/Rivista

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S

Anno di pubblicazione

2013

ISSN

1937-1632

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

17

Ultimo Aggiornamento Citazioni

2017-04-23 03:20:56

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile