Quantum States and Complex Projective Space

Details Quantum States and Complex Projective Space Quantum States and Complex Projective Space

2007-01-05

arxiv.org/abs/math-ph/0701011v2

Physics

Mathematical Physics

7 pages; some minor errors about format and typing are corrected

Scientific paper

In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through analyzing some of the basic principles and concepts of quantum mechanics, including the principle of superposition, representations and inner product of quantum states, and give some interesting examples. Based on our point of views we are able to generate the evolution equation of quantum states -- the Heisenberg equation. We also discuss the act of dynamical operators on quantum states.

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