Quantum mechanics in the general quantum systems (V): Hamiltonian eigenvalues

Details Quantum mechanics in the general quantum systems (V): Hamiltonian eigenvalues Quantum mechanics in the general quantum systems (V): Hamiltonian eigenvalues

2009-11-02

arxiv.org/abs/0911.0347v1

Physics

Quantum Physics

18 pages, No figure. This is the fifth manuscript. Previous manuscripts see arXiv:quant-ph/0611216, arXiv:quant-ph/0611217,

Scientific paper

We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of eigenvalues of arbitrary Hamiltonian via solving an algebra equation satisfied by a kernal function, which involves the contributions from all order perturbations. In order to verify the validity of our expressions and reveal the power of our approach, we calculate the ground state energy of a quartic anharmonic oscillator and have obtained good enough results comparing with the known one.

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