![]() ⟨ ψ | ϕ ⟩ ∈ C is the scalar product of vectors | ψ⟩ and | ϕ⟩. Ψ | ∈ H represents a vector of the dual Hilbert space of H (a row vector). ![]() ![]() | ψ ∈ H represents a vector of the Hilbert space H (a column vector). H represents a Hilbert space, usually the space of pure states of a system. The problems proposed are solved by the use of Mathematica notebooks that can be found in Ref. To deepen the techniques of solving the Lindblad equation, an example consisting of a two-level system with decay is analyzed, illustrating the content of every section. VI is devoted to the resolution of the master equation using different methods. V, we define the concept of completely positive and trace-preserving maps (CPT-maps), we derive the Lindblad master equation from two different approaches, and we discus several properties of the equation. Section IV includes a description of a mathematical framework, the Fock-Liouville space (FLS) that is especially useful to work in this problem. III, there is a brief review of quantum mechanical concepts that are required to understand the paper. II, the mathematical requirements are introduced, while in Sec. The purpose of this paper is to provide basic knowledge about the Lindblad master equation.
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