论文标题
光谱定理方法的量子观察值II的特征功能
Spectral Theorem approach to the Characteristic Function of Quantum Observables II
论文作者
论文摘要
我们计算反交换器操作员的分解$ XP+PX $和量子谐波振荡器Hamiltonian Operator $ \ frac {1} {2} {2}（x^2+p^2）$。使用Stone的公式在Hilbert空间上找到AN的光谱分辨率，即有界或无界的自动伴侣操作员，我们还计算了它们的真空特性功能（量子傅立叶变换）。我们还展示了如何将Stone的公式应用于有限尺寸量子可观察物的真空特性功能的计算。该方法被认为是依靠相关的代数换向关系的代数（或海森堡）方法的分析替代方法。
We compute the resolvent of the anti-commutator operator $XP+PX$ and of the quantum harmonic oscillator Hamiltonian operator $\frac{1}{2}(X^2+P^2)$. Using Stone's formula for finding the spectral resolution of an, either bounded or unbounded, self-adjoint operator on a Hilbert space, we also compute their Vacuum Characteristic Function (Quantum Fourier Transform). We also show how Stone's formula is applied to the computation of the Vacuum Characteristic Function of finite dimensional quantum observables. The method is proposed as an analytical alternative to the algebraic (or Heisenberg) approach relying on the associated Lie algebra commutation relations.
