本文使用變換設計方法設計長橢球型量子斗篷，得到物質波在斗篷區的等效質量和等效位能，便可引導物質波的行進方向，創造出一個長橢球型的隱藏區，其隱藏區為封閉的有限空間，此斗篷是第一個三維非球對稱的量子斗篷。

A quantum cloak with the prolate spheroidal shape is designed by using the method of transformation design. The mass parameters and effective potential in the cloaking shell for a perfect cloaking of a probing matter wave are given. With the current viewpoint of quantum cloaking developed in our group recently, we show that the presented spheroidal cloak can perfectly guide the matter wave in the situation of any oblique incidence. The proposed spheroidal quantum cloak provides the first three dimensional non-spherical setup of quantum cloaking.

論文審定書 i
致謝 ii
中文摘要 iii
Abstract iv
第一章 緒論 1
第二章 量子隱形斗篷設計原理 4
2.1三維正交坐標系 4
2.2廣義坐標系 10
第三章 Prolate Spheroidal function 12
第四章 長橢球型量子隱形斗篷 19
4.1長橢球型量子斗篷的等效質量與等效位能 19
4.2長橢球型量子斗篷的機率流密度 25
4.3長橢球型量子斗篷的數值模擬 30
4.4長橢球型量子斗篷的節點與節點線 36
4.5長橢球型量子斗篷的極限條件 40
第五章 結論 49
參考文獻 50
附錄A Prolate Spheroidal Function相關推導 51
A.1 推導Recurrence Relation 51
A.2 推導Transcendental equation 55
附錄B 以Prolate Spheroidal Function展開平面波 58
B.1 Plane Wave Expansion 58
B.2 Wronskian 65

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