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- All Subjects: Quantum Mechanics
- Creators: Comfort, Joseph
- Creators: Kotschwar, Brett
- Resource Type: Text
- Status: Published

Chapter 1 introduces some key elements of important topics such as; quantum mechanics,

representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´

tivistic wave equations that will play an important role in the work to follow. In Chapter 2,

a complex covariant form of the classical…

Chapter 1 introduces some key elements of important topics such as; quantum mechanics,

representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´

tivistic wave equations that will play an important role in the work to follow. In Chapter 2,

a complex covariant form of the classical Maxwell’s equations in a moving medium or at

rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum

tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its

connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´

netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.

Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s

equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell

and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´

operators of the Poincare group. A connection between the spin of a particle/field and ´

consistency of the corresponding overdetermined system is emphasized in the massless

case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which

is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨

evolution of exact wave functions of the generalized harmonic oscillators is determined

in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is

shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem

for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the

methods introduced in Chapter 5 a model for the quantization of an electromagnetic field

in a variable media is analyzed. The concept of quantization of an electromagnetic field

in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode

of radiation for this model is used to find time-dependent photon amplitudes in relation

to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the

uncertainty relation, are explicitly given in terms of the Ermakov-type system.

The longstanding issue of how much time it takes a particle to tunnel through quantum barriers is discussed; in particular, the phenomenon known as the Hartman effect is reviewed. A calculation of the dwell time for two successive rectangular barriers in the opaque limit is given and the result depends…

The longstanding issue of how much time it takes a particle to tunnel through quantum barriers is discussed; in particular, the phenomenon known as the Hartman effect is reviewed. A calculation of the dwell time for two successive rectangular barriers in the opaque limit is given and the result depends on the barrier widths and hence does not lead to superluminal tunneling or the Hartman effect.

This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal…

This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.