Linking Scalar Elastodynamics and Non-Hermitian Quantum Mechanics

Relativistic Non-Hermitian Quantum Mechanics

We develop relativistic wave equations in the framework of the new non-hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT -symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no cou...

Neutrino Oscillations and Non-Hermitian Quantum Mechanics

In this dissertation we firstly present a brief review of the Standard Model of particle physics, focussing on aspects of the model that prove most relevant in the context of explaining the observed oscillation of neutrinos. The phenomenology of neutrino oscillations is then introduced, and different possible extensions to the Standard Model that would allow for non-zero neutrino masses, thereb...

Pseudo-Hermitian Quantum Mechanics

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of t...

Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems

Annihilation and creation operators in non-Hermitian supersymmetric quantum mechanics

Harmonic oscillators with a centrifugal spike are analysed, via a non-Hermitian regularization, within a complexified SUSY quantum mechanics. The formalism enables us to construct (factorize) the creation and annihilation operators. We show how the real (though, generically, non-equidistant) spectrum complies with the current SUSY-type isospectrality (degeneracy) in an unusual way. e-mail: znoj...