在這篇論文中，我們採用延續法（PACM）來計算自旋為1 的
玻色-愛因斯坦凝聚（BEC）的約費-朴立卻德磁場下的基態
和激發態解。把自旋無關的作用力、自旋交換的作用力與約
費-朴立卻德強度磁場為延續法的參數。特別是線性薛丁格
方程（LSE）為延續法的起始點。最後比較相對應的能量，
我們可以在約費-朴立卻德磁場影響下自旋為1 下的基態。

In this thesis, we employ the parameter switching continuation
methods (PACM) to compute the ground and excited state solutions of
the spin-1 Bose Einstein condensates (BEC) with the Ioffe-Pritchard
magnetic field.
The spin-independent and spin-exchange coupling constants and the
strength of Ioffe-Pritchard magnetic field are treated as the continuation
parameters. Particularly, the ground and excited state solutions of the
linear Schrödinger equation (LSE) which describes the BEC system
without any interaction are used as the starting points in the
continuation process. Finally, by comparing the corresponding energies,
we can obtain the ground state of the spin-1 BEC under the effect of the
Ioffe-Pritchard magnetic field.

1. Introduction 1
2. Model Description 3
3. Numerical Schemes 8
3.1. Pseudo-Arclength Continuation Method 8
3.2. Starting Points in Continuation Process 10
4. Numerical Results 13
4.1. The case of B(x) = cos(x) + isin(x), gn = 400, and gs = 250 13
4.2. The case of B(x) = cos(x) + isin(x), gn = 400; and gs = -250 15
4.3. The case of B(x) = cos(x) + icos(x), gn = 400, and gs = 250 18
4.4. The case of B(x) = cos(x) + icos(x), gn = 400, and gs = -250 20
4.5. Effect of gs 23
5. Conclusion 26

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