Quantum States
A quantum state is the condition a quantum mechanical system is in. The state is usually described by a wave function. It is different from classical states of systems in that the quantum system has separate, discrete levels, whereas the states of a classical system are continuous. This means that a particle can move from one quantum state to another without ever being in a state in between. The discrete steps are known as quantization.
A quantum leap or jump is the transition between quantum states. Although colloquial usage varies, quantum leaps are almost always very small--only a fraction of the system's total energy. These quantum state changes are responsible for common phenomena like light emission from atoms. They can occur spontaneously (as in radioactive decay) or can be stimulated to occur (as in lasers).
Each quantum mechanical system has special stationary states known as eigenstates. The eigenstates give mathematical expressions for the quantized states possible for the system. Eigenstates can be finite or infinite in number: for example, electrons can have spin up or spin down, but there are infinitely many positions for a particle to occupy in free space. The eigenstates are a basis set: that is, all other states can be expressed in terms of the eigenstates. This expression is sometimes called a superposition of states, in which each state has some percentage of each eigenstate. The most famous superposition experiment is that of Schrödinger's cat, where the eigenstates of "alive" and "dead" are superimposed.
When a quantum mechanical state is observed, the system is forced into one or another of the eigenstates. The total state prior to observation could be expressed in terms of the probability a system has of being in each eigenstate. After observation, the system is only in one of them. In the famous Schrodinger's cat example, only "alive" or "dead" are permitted to be the observed eigenstates. The state may be changed and evolve after observation, but it may only be observed in an eigenstate.
There are some state measurements which are incompatible. For example, position and momentum cannot simultaneously have their state determined precisely. This principle is known complementarity; the measurements are complementary or conjugate measurements. Complementarity of state measurements derives from Heisenberg's Uncertainty Principle.
The idea of quantum states is useful for expressing the instantaneous behavior of a system, as well as for analyzing potential modes of behavior for it. Each of the eigenstates corresponds to a potential measured reality, and can be seen in the lab.
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