题目内容
（请给出正确答案）
粒子的态密度D(ε)定义为：D(ε)dε代表粒子的能量处于ε与ε+dε之间的量子态数(见§7.15)．这里只考虑粒子的平动自由度所对应的态密度．
(i)设粒子的能谱(即能量与动量的关系)是非相对论性的，试分别对下列三种空间维数，求相应的态密度D(ε)：
(a)粒子局限在体积为V的三维空间内运动，
(b)粒子局限在面积为A的二维平面内运动，
(c)粒子局限在长度为L的一维空间内运动，
(ii)设粒子的能谱是极端相对论性的，即ε=cp，
在完成计算后，读者可以列表小结一下，从中可以看出D(ε)与粒子能谱及空间维数的关系．
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