论文标题
两个旋转的颗粒通过两体高斯电势相互作用，并在两个空间尺寸中固定限制
Two rotating particles interacting via two-body Gaussian potential harmonically confined in two spatial dimensions
论文作者
论文摘要
我们研究了两个通过两体高斯电势相互作用的无旋转玻色子，这些电势经受了围绕在两空间尺寸的谐波陷阱中的轴的外部印象深刻的旋转。我们获得了相对角动量$ | m | $状态的先验方程，具有两体相互作用范围的各种值$σ$和两体相互作用强度$ g_ {2} $，以研究产生的能量谱并分析希尔伯特太空尺寸的作用$ \ didetilde $ \ didetilde {N n} $。我们比较了$δ$功能潜力的有吸引力和排斥相互作用的结果，以及对于各种相互作用范围值的高斯潜力。我们研究相互作用参数和相对角动量对基态能及其各种组分的影响，即动能，陷阱电位和相互作用潜力。对于给定的$ | M | $和非相互作用的情况，我们观察到基态能量独立于相互作用范围。但是，对于给定的相对角动量和相互作用强度$ g_ {2}> 0 $，基态能量增加，相互作用范围的增加。在交互强度的下方$ g_ {2} v（r）\ leq -1 $，基态能量与$ | m | = 0 $状态的物理上不可接受的负性分歧。此外，对于$ | m | = 1 $，基态能量变得独立于相互作用强度。对于$ | m | $，我们提出了高斯交互潜力与$δ$功能潜力之间的比较研究。此外，我们观察到，对于给定的$ g_ {2} $和$ | m | $，对于$δ$ - 功能电位{\ it I.E.} $σ\至0 $，为了实现基态能量的融合，我们需要一个相当大的关键Hilbert Space。而对于$σ\至1 $的高斯相互作用潜力的情况，基态能量会收敛着相当小的关键希尔伯特空间。
We study two spinless bosons interacting via two-body Gaussian potential subjected to an externally impressed rotation about an axis confined in a harmonic trap in two-spatial dimensions. We obtain a transcendental equation for the relative angular momentum $|m|$ state with various values of the two-body interaction range $σ$ and the two-body interaction strength $g_{2}$ to study the resulting energy spectrum and analyze the role of Hilbert space dimensions $\widetilde{N}$. We compare results for both attractive and repulsive interaction for $δ$-function potential and Gaussian potential for various values of interaction range. We study the effects of interaction parameters and relative angular momentum on the ground state energy and its various components, namely, kinetic energy, trap potential and interaction potential. For a given $|m|$ and non-interacting case, we observe that the ground state energy becomes independent of interaction range. However, for a given relative angular momentum and interaction strength $g_{2}>0$, there is an increase in ground state energy with an increase in interaction range. Below the interaction strength $g_{2}V(r)\leq -1$, ground state energy diverges to physically unacceptable negative-infinity for $|m|=0$ state. Further, for $|m|=1$, the ground state energy becomes independent of the interaction strength. For a $|m|$, we present a comparative study between the Gaussian interaction potential and the $δ$-function potential. Further, we observe that for a given $g_{2}$ and $|m|$, for $δ$-function potential {\it i.e.} $σ\to 0$, to achieve the convergence of ground state energy, we require a considerably large critical Hilbert space. Whereas, in the case of Gaussian interaction potential with $σ\to 1$, the ground state energy converges for a considerably small critical Hilbert space.
