Fundamentals of Quantum Mechanics in Liouville Space
- URL: http://arxiv.org/abs/2003.11472v3
- Date: Wed, 18 Nov 2020 09:51:53 GMT
- Title: Fundamentals of Quantum Mechanics in Liouville Space
- Authors: Jerryman A. Gyamfi
- Abstract summary: This paper articulates a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space.
One of the greater strengths of the formalism expatiated on here is the striking similarities it bears with Dirac's bra-ket notation.
For the purpose of illustrating how the formalism can be effectively employed, we use it to solve a quantum optical master equation for a two-level quantum system.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The purpose of this paper is to articulate a coherent and easy-to-understand
way of doing quantum mechanics in any finite-dimensional Liouville space, based
on the use of Kronecker product and what we have termed the `bra-flipper'
operator. One of the greater strengths of the formalism expatiated on here is
the striking similarities it bears with Dirac's bra-ket notation. For the
purpose of illustrating how the formalism can be effectively employed, we use
it to solve a quantum optical master equation for a two-level quantum system
and find its Kraus operator sum representation. The paper is addressed to
students and researchers with some basic knowledge of linear algebra who want
to acquire a deeper understanding of the Liouville space formalism. The
concepts are conveyed so as to make the application of the formalism to more
complex problems in quantum physics straightforward and unencumbered.
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