ANALISIS PERSAMAAN DIRAC MENURUT PARADIGMA LAGRANGE DAN BEBERAPA PENERAPANNYA (ANALYSIS OF DIRAC EQUATION VIA LAGRANGE PARADIGM AND SOME OF ITS APPLICATIONS)
| Main Author: | Perpustakaan UGM, i-lib |
|---|---|
| Format: | Article NonPeerReviewed |
| Terbitan: |
[Yogyakarta] : Universitas Gadjah Mada
, 2001
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| Subjects: | |
| Online Access: |
https://repository.ugm.ac.id/25540/ http://i-lib.ugm.ac.id/jurnal/download.php?dataId=8536 |
Daftar Isi:
- ABSTRACT Dirac equation is a wave equation for a relativistic charged particle with momentum p, mass m, spin-1/2 and subjected to an external potential. Its can be derived form Pauli formulation for spin 1/2 particle and then generalize into the relativistic case yields four-spinor wave equation. Solution of the Dirac equation for free particles with arbitrary momentum -0 yields plane waves spinors with an energy eigenvalue either E =-- 44p2c2 +m2c4 and E= Thip2c2 +m2c4 Lagrange paradigm I and II used for diagonalizing the Dirac equation for a general potential. Its results a diagonal hamiltonian which contains separate block/partition with positive energy eigenvalue and negative energy eigenvalue. From this hamiltonian, one can identify various expansion of the relativistic kinetic energy, electrostatic energy, dipole magnet energy, spin-orbit interaction and the Darwin term which the same as result of the Flody-Wouthuysen transformation. Application of the Dirac equation for hydrogen-like atoms is done by solving the corresponding equation which contains the Coulomb potential as the potential energy term. Its methods of solution hew closer to the more familiar solution of the nonrelativistic Schrodinger equation for Coulombic wave functions. In this way, one get the electronic hydrogen-like wave function for bound states (E 5 m) and scattering states (E m). From the bound state solution, the ground state wave function of hydrogen-like atom with spin-up and spin-down could be written explicitly and investigated thoroughly. The fine structure, hyperfine structure and Lamb Shift for hydrogen atom have been calculated. According to the theory fine structure between 2P3,2 and 211,2 states and hyperfine structure between triplet and singlet states are 10,9 GHz and 1420 MHz , respectively. Lamb shift of 2S112 � 2131/2 is 660 MHz . The difficulties raised by the negative energy eigenstates can be clarified by introducing the Hole Theory. This theory indicates the existence of positron as antiparticles of electron with the same mass and spin but having opposite charges. Dirac equation can also used to explain the existence and dynamics of neutrino and antineutrino. Key Words : Dirac, spinor relativistic, hamiltonian, hydrogen-like atoms, hole