Abstract
A study of the band structure of a massless particle in a cosine potential is made via the Dirac equation. It is shown that every alternate band gap disappears as a consequence of a periodicity of the potential combined with a peculiar symmetry of the Dirac equation. This basic potential is then used to study a simple one-dimensional model of the nucleus from which it is ascertained that modelling the mean field of the quarks in the nucleus via a pure scalar potential is unsatisfactory. A simple extension involving a combined scalar and vector potential is then proposed as a possible solution to this problem. The effect of the addition of this vector component to the band structure is also investigated. 32 refs.
Citation Formats
Clerk, G J, and McKellar, B H.J.
Band gaps for the relativistic Mathieu potential.
Australia: N. p.,
1992.
Web.
Clerk, G J, & McKellar, B H.J.
Band gaps for the relativistic Mathieu potential.
Australia.
Clerk, G J, and McKellar, B H.J.
1992.
"Band gaps for the relativistic Mathieu potential."
Australia.
@misc{etde_10109140,
title = {Band gaps for the relativistic Mathieu potential}
author = {Clerk, G J, and McKellar, B H.J.}
abstractNote = {A study of the band structure of a massless particle in a cosine potential is made via the Dirac equation. It is shown that every alternate band gap disappears as a consequence of a periodicity of the potential combined with a peculiar symmetry of the Dirac equation. This basic potential is then used to study a simple one-dimensional model of the nucleus from which it is ascertained that modelling the mean field of the quarks in the nucleus via a pure scalar potential is unsatisfactory. A simple extension involving a combined scalar and vector potential is then proposed as a possible solution to this problem. The effect of the addition of this vector component to the band structure is also investigated. 32 refs.}
place = {Australia}
year = {1992}
month = {Dec}
}
title = {Band gaps for the relativistic Mathieu potential}
author = {Clerk, G J, and McKellar, B H.J.}
abstractNote = {A study of the band structure of a massless particle in a cosine potential is made via the Dirac equation. It is shown that every alternate band gap disappears as a consequence of a periodicity of the potential combined with a peculiar symmetry of the Dirac equation. This basic potential is then used to study a simple one-dimensional model of the nucleus from which it is ascertained that modelling the mean field of the quarks in the nucleus via a pure scalar potential is unsatisfactory. A simple extension involving a combined scalar and vector potential is then proposed as a possible solution to this problem. The effect of the addition of this vector component to the band structure is also investigated. 32 refs.}
place = {Australia}
year = {1992}
month = {Dec}
}