Abstract
The Non-Hermitian aspect of Quantum Mechanics has been of great interest recently. There have been numerous studies on non-Hermitian Hamiltonians written for natural processes. Some studies have even expressed the hydrogen atom in a non-Hermitian basis. In this paper the principles of non-Hermitian quantum mechanics is applied to both the time independent perturbation theory and to the time dependant theory to calculate the Stark effect. The principles of spherical harmonics has also been used to describe the development in the non-Hermitian case. Finally, the non-Hermitian aspect has been introduced to the well known Stark effect in quantum mechanics to find a condition in which the Stark effect will still be true even if a non-Hermitian Hamiltonian is used. This study completes the understanding at a fundamental level to understand the well known Stark effect. Doi: 10.28991/esj-2020-01242 Full Text: PDF
Highlights
The most successful theory which we have till id quantum mechanics
This means that the quantum mechanical operators which expresses the behavior of a quantum system are Hermitian
There have been numerous studies which describe the application of non-Hermitian quantum mechanics to calculate matrices and eigen values which is an important way to understand the mathematical aspects of quantum mechanics [3, 6, 13]
Summary
The most successful theory which we have till id quantum mechanics. The predictions made by quantum mechnics has been corroborated by the various experiments ranging from low energy experiments to high energy experiments. It has been seen [1] that H does not necessarily have to be Hermitian to necessarily obtain a real energy eigenvalue spectra This gives us the opportunity to study and understand the aspects of quantum mechanics related with nonHermitian operators as well, which is known as PT-symmetry theory [1]. This paper studies the non-Hermitian Hamiltonian as described in Bender (2005), Hamazaki et al (2020), Ernzerhof et al (2020), Romero et al (2013) and Bagarello and Gargano (2020) [1, 3, 5, 10, 11] and studies the spherical harmonics and hydrogen atom through the PT-symmetry theory This is applied to the well known result of time-independent perturbation theory in quantum mechanics and the very well known Stark effect
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