最小长度测不准关系下V型势场中粒子的位置和动量测不准
Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
摘要：
当位置和动量算符满足变形对易关系[x，p]=i \hbar（1+βp^2），β>0时，计算了一维势V（x）= FPDMATHABMM，F>0中粒子位置和动量的不确定度.在谐振子的情况下，这是在以前的出版物中研究，哈密顿量H_1 = p^2/2 m + F |x|承认离散的正能量本征态的正和负的质量。正质量态的不确定度表现为Δx ~ 1/Δp（β=0极限）。然而，对于负质量态，与我们有Δx ~ Δp的谐振子情况相反，Δx和Δp都发散。我们认为负质量态的存在性及其不确定性的发散性可以通过理论的经典极限来理解。我们的结果进行了比较与以前的工作Benczik。
英文摘要：
We calculate the uncertainties in the position and momentum of a particle in the 1D potential V(x)=F|x|, F>0, when the position and momentum operators obey the deformed commutation relation [x,p]=i\hbar(1+βp^2), β>0. As in the harmonic oscillator case, which was investigated in a previous publication, the Hamiltonian H_1 = p^2/2m + F|x| admits discrete positive energy eigenstates for both positive and negative mass. The uncertainties for the positive mass states behave as Δx ~ 1/Δp as in the β=0 limit. For the negative mass states, however, in contrast to the harmonic oscillator case where we had Δx ~ Δp, both Δx and Δp diverge. We argue that the existence of the negative mass states and the divergence of their uncertainties can be understood by taking the classical limit of the theory. Comparison of our results is made with previous work by Benczik.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
