Plávala Martin, Kleinmann Matthias
Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany.
Faculty of Physics, University of Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany.
Phys Rev Lett. 2022 Jan 28;128(4):040405. doi: 10.1103/PhysRevLett.128.040405.
We show how to construct general probabilistic theories that contain an energy observable dependent on position and momentum. The construction is in accordance with classical and quantum theory and allows for physical predictions, such as the probability distribution for position, momentum, and energy. We demonstrate the construction by formulating a toy model for the harmonic oscillator that is neither classical nor quantum. The model features a discrete energy spectrum, a ground state with sharp position and momentum, an eigenstate with a nonpositive Wigner function as well as a state that has tunneling properties. The toy model demonstrates that operational theories can be a viable alternative approach for formulating physical theories.
我们展示了如何构建包含依赖于位置和动量的能量可观测量的一般概率理论。该构建符合经典理论和量子理论，并允许进行物理预测，例如位置、动量和能量的概率分布。我们通过构建一个既非经典也非量子的谐振子玩具模型来演示该构建过程。该模型具有离散能谱、具有确定位置和动量的基态、具有非正维格纳函数的本征态以及具有隧穿特性的态。这个玩具模型表明，操作理论可以成为构建物理理论的一种可行替代方法。
