One-particle Systems
In general, the one-particle state could be described by a complete set of quantum numbers denoted by . For example set of the three quantum numbers associated to an electron in a coulomb potential, for example the hydrogen atom. Hence, the state is called and is an eigenvector of the Hamiltonian operator. One can obtain a state function representation of the state using . All eigenvectors of an Hermitian operator form a complete basis, so one can construct any state obtaining the completeness relation:
All the properties of the particle could be known using this vector basis.
Read more about this topic: First Quantization
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