Spectral Analysis of a Quantum Harmonic Oscillator Coupled to Infinitely Many Scalar Bosons
Spectral Analysis of a Quantum Harmonic Oscillator Coupled to Infinitely Many Scalar Bosons
复制标题
与无穷多个标量玻色子耦合的量子谐波振荡器的谱分析
DOI：
10.1016/0022-247x(89)90108-x
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发表时间：
1989
影响因子：
2.4
通讯作者：
A. Arai
中科院分区：
文献类型：
--
作者：
A. Arai
我们分析了量子谐振子与无限多个标量玻色子相互作用模型的Hamilton量的谱性质。哈密顿量给出了无限维薛定谔型算子嵌入本征值的扰动问题的一个例子。它明确地表明，嵌入的本征值的自由（未扰动）的哈密顿量并不总是消失的相互作用（扰动）和消失或嵌入的本征值的稳定性取决于所包含的参数的哈密顿量。
We analyze the spectral property of the Hamiltonian for a model of a quantum harmonic oscillator interacting with infinitely many scalar bosons. The Hamiltonian gives an example of perturbation problem of embedded eigenvalues with infinite dimensional Schrödinger's type operators. It is shown explicitly that the embedded eigenvalues of the free (unperturbed) Hamiltonian do not always disappear under the interaction (perturbation) and the disappearance or the stability of the embedded eigenvalues depends on the parameters contained in the Hamiltonian.