Quantum Theory of Anharmonic Oscillators : Some Exact Relations between Matrix Elements and Their Use for Various Approximation Methods

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概要

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• This is an investigation of an anharmonic oscillator characterized by the potential (ω_0^2/2)q^2+λ'q^4. By using the exact relations obtained by evaluating <i|[H, O]|_±|j> where O is an arbitrary operator, H is our total Hamiltonian and |i> and |j> are exact eigenstates of H, we derive an exact recurrence formula. This formula allows us to express τ-functions with a higher power of the variables through τ-functions with a lower power of the variables and energy eigenvalues. In this way we derive several exact relations, which are, in a sense, generalizations of the virial theorem and sum rules (Eqs. (4・5), (4・6) and (5・4)). These exact relations are the central equations of this paper. On the basis of these exact relations we propose our "nearest neighbour level" (N.N.L) approximation, which seems to provide a good approximation scheme. We can also use our exact relations to test the validity of various approximation methods, and as an example, we discuss the "New-Tamm-Dancoff" (N.T.D)-type of approximation in detail.

• 理論物理学刊行会の論文
• 1983-09-25

著者

• Yamazaki Kazuo

  Institut Fur Theoretische Physik Der Universitat Graz:physics Department College Of General Educatio

• YAMAZAKI Kazuo

  Institut fur Theoretische Physik der Universitat Graz:Physics Department, College of General Education Kyoto University

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• Quantum Theory of Anharmonic Oscillators : Some Exact Relations between Matrix Elements and Their Use for Various Approximation Methods
• A Comment on a Paper of Blomer

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