Size-quantization levels of an exciton in large nanocrystals is studied theoretically. For the nanocrystal size, $L$, much bigger than the Bohr radius, $a_B$, the level positions do not depend on $a_B$. The correction to the levels in a small parameter $a_B∕L$ depends on the reflection phase of the exciton from the boundary. Calculation of this phase constitutes a three-body problem: electron, hole, and the boundary. This calculation can be performed analytically in the limit when the hole is much heavier than the electron. Physically, a slow motion of the hole towards the boundary takes place in the effective potential created by the fast motion of the electron orbiting the hole and touching the boundary. As a result, the hole is reflected before reaching the boundary. The distance of the closest approach of the hole to the boundary (the dead layer) exceeds $a_B$ parametrically.

理论上研究了大纳米晶体中激子的尺寸量子化水平。对于纳米晶体尺寸，$\mathrm{大号}$比玻尔半径大得多 ${\mathrm{一个}}_{乙}$，级别位置不取决于 ${\mathrm{一个}}_{乙}$。用小参数校正水平${\mathrm{一个}}_{乙}∕\mathrm{大号}$取决于激子从边界的反射相位。计算该相构成了一个三体问题：电子，空穴和边界。当空穴比电子重得多时，可以在极限条件下以解析方式执行此计算。在物理上，空穴向边界的缓慢运动是在有效电势中发生的，该有效电势是由绕该轨道运动并接触边界的电子的快速运动产生的。结果，孔在到达边界之前被反射。孔最靠近边界（死层）的距离超过${\mathrm{一个}}_{乙}$ 参数化地。