Dirac particle in a box, and relativistic quantum Zeno dynamics

Lawrence S. Schulman

Jambul Yusupov, D.M. Otajanov, V. E. Eshniyazov +1 more

Parsa Hossein Ghorbani, Varqa Abyaneh

Kamran Ullah, Jameel Hussain, Mustafa Khan

Present work is devoted to studying the spatio-temporal of the Dirac and the Klein Gordon (KG) particles confined in a one-dimensional box. We discuss the quantum carpets and revivals time for each particle. Moreover, we explain that the relativistic phenomena not only decrease the density of the corresponding carpets but also affect the revivals time of each particle within a box. Further, we impose different limiting conditions on the obtained Dirac energy solution and explain the wellknown slight-relativistic and non-relativistic quantum carpets, respectively. In addition, we extend our study to explain the quantum carpets of the KG particle at different energy states and compare its revivals time with the Dirac particle.

Emil Blomquist, Trotte Boman

The Dirac equation is a relativistic wave equation and was the first equation to capture spin in relativistic quantum mechanics. Here, the Dirac equation will be derived and solved for a particle in a spherical box potential. Comparisons to the non-relativistic Schrödinger equation as well as to a relativistically corrected Schrödinger equation will be made. Applications of the Dirac equation, such as the Bogoliubov model, are examined and discussed and it is validated that the Dirac equation can provide knowledge about elementary particles.