Staudte, Donald Stephen

### Description

This thesis is concerned with the development of a new spin-1/2 wave equation
in relativistic quantum mechanics. This equation is the spin-1/2 analogue
of the spin-0 Feshbach-Villars equation.
The thesis begins in chapter 1 with a review of the subject of relativistic
wave equations and its place in the development of modern physics. Chapter
2 sees the derivation of the new equation (hereafter referred to as the FV1/2
equation). This derivation is presented at three levels of...[Show more] understanding, and
is combined with an analysis of the equation using elements of the underlying
mathematics of the theories of special relativity and quantum mechanics. The
analysis justifies the methods of derivation of the equation, and its suitability as
a wave equation in relativistic quantum mechanics. It is shown th a t the FV1/2
equation is different to the Dirac equation and other equations in the literature.
One of the striking features of the FV1/2 equation is th a t it contains a less
restrictive dynamics than the conventional Dirac equation. Chapter 3 examines
the solution space and proves some results using the discrete symmetries C,
P and T, which enable a subset of the solution space to be used for physical
applications. It is possible to use a subset of solutions which contain the usual
Dirac negative energy states, or it is possible to use a subset which contains only
positive energy states, but includes states of opposite signs of charge. The second
subset corresponds to the physical properties of particles and antiparticles and
suggests th a t the FV1/2 equation could be useful in atomic physics.
Chapter 4 represents a start on the development of the FV1/2 equation for
use in atomic physics. It contains a study of hydrogenic atoms. The energy
spectra and wavefunctions for hydrogenic atoms are derived using the FV1/2
equation. The method of solution is of comparable difficulty to th a t using the
Dirac equation. The spectra are found to be identical to th a t of the Dirac
equation, but the wavefunctions differ. A calculation of the expectation value of
the Coulomb energy is performed and the results obtained differ from the Dirac
equation results by 6 x 10-3% for Z — 1, and 40% for Z = 70. This suggests
th a t physically measureable quantities should be calculated and compared using
the FV1/2 and Dirac equations. A calculation is presented to show the energy
spectra and wavefunctions obtained are consistent with the literature. The results obtained in this chapter (again) suggest th a t the FV1/2 equation could be useful
for calculations in atomic physics.
Chapter 5 discusses important further work which should be undertaken if
the FV1/2 equation is to become useful to physics. The development in the
previous chapters concentrated on the FV1/2 equation in relativistic quantum
mechanics. It should be also considered as a quantised field equation. The two
electron problem and the calculation of physical quantities are crucial tests of
the FV1/2 equation’s applicability in atomic physics. The mathematical analysis
in chapter 2 can be extended. Suggestions for gaining a deeper mathematical
understanding of the less restrictive dynamics of the FV1/2 equation are given.
Finally some conclusions on what has been achieved in the thesis are presented
in chapter 6.

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