中文摘要：

导出了新的Plücker关系式，利用Wronskian技巧和Plücker关系式证明著名的Crum定理．给出了Crum定理一个新的简洁证明．在附录中证明了三个Plücker关系式．

英文摘要：

The Wronskian determinant technique and Plücker relations are used to prove the famous Crum theorem. A new and concise proof of the Crum theorem is given. Some new Plücker relations are proved in appendix.