Quantum Rings are defined to be polygons with sides all of the same unit length that are connected with a fixed positive or negative angle. In the research, the number of Quantum Rings corresponding to a given number of sides and a fixed angle will be discussed. Quantum Rings could be expressed by many sequences which would involve the theory of partitions and ways to eliminate the many to one nature of the sequences in order to evaluate the upper and lower bound. Besides estimating the upper and lower bound, a lot of the qualities of the Quantum Rings under certain circumstances will be mentioned.「能量環」為許多單位長度的線段以定角首尾相接，並且最後接回原點的多邊形。本研究將要探討對於給定邊長個數與相接角度的「能量環」的個數。「能量環」可以被表示成許多種數列的形式。在數列的運算中會牽涉到許多數字分割的理論與排列組合的排除重複以求得能量環個數的上下界。除了定量的求算出上下界以外，報告中也定性的歸納出許多給予特殊條件的能量環的性質。
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