Abstract
Quantum theory is based on the following axioms1:
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1.
The state of a system is described by a state vector |ψ〉 in a linear space.
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2.
The observables are represented by hermitian operators A…, and functions of observables by the corresponding functions of the operators.
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3.
The mean (expectation) value of an observable in the state|ψ〉 is given by 〈A〉 = 〉ψ| A |ψ〉.
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4.
The time evolution is determined by the Schrödinger equation involving the Hamiltonian H
$${\text{i}}\hbar \frac{{\partial \left| \psi \right\rangle }}{{\partial t}} = H\left| \psi \right\rangle $$(5.1.1) -
5.
If, in a measurement of the observable A, the value a n is found, then the original state changes to the corresponding eigenstate |n〉 of A.
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© 1999 Springer-Verlag Berlin Heidelberg
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Schwabl, F. (1999). Relativistic Wave Equations and their Derivation. In: Advanced Quantum Mechanics. Advanced Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03929-8_5
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DOI: https://doi.org/10.1007/978-3-662-03929-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03931-1
Online ISBN: 978-3-662-03929-8
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