Two-state quantum system
In quantum mechanics, a two-state system (also known as a two-level system) is a system that can exist in any quantum superposition of two independent (physically distinguishable) quantum states. The Hilbert space describing such a system is two-dimensional. Therefore, a complete basis spanning the space will consist of two independent states.
Two-state systems are the simplest quantum systems that can exist, since the dynamics of a one-state system is trivial (i.e. there is no other state the system can exist in). The mathematical framework required for the analysis of two-state systems is that of linear differential equations and linear algebra of two-dimensional spaces. As a result, the dynamics of a two-state system can be solved analytically without any approximation.
A very well known example of a two-state system is the spin of a spin-1/2 particle such as an electron, whose spin can have values +ħ/2 or −ħ/2, where ħ is the reduced Planck constant. Another example, frequently studied in atomic physics, is the transition of an atom to or from an excited state; here the two-state formalism is used to quantitatively explain stimulated and spontaneous emission of photons from excited atoms.
The state of a two-state quantum system can be represented as vectors of a two-dimensional complex Hilbert space, this means every state vector is represented by two complex coordinates.
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