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# 物理代考| Hilbert Space量子力学代写

## 物理代写

9.1 Hilbert Space
Ordinary three-dimensional vectors have cartesian components, and a dot product defined by
\begin{aligned} \vec{v} &=\left(v_{1}, v_{2}, v_{3}\right) \ \vec{a} \cdot \vec{b} &=\sum_{i=1}^{3} a_{i} b_{i} \end{aligned}
Let us generalize this in two ways:

• Extend the space to have an infinite number of dimensions;
• Let the components of the vector become complex.
75
76 One then has
Introduction to Quantum Mechanics
The square of the length of the vector is then given by
$$|\vec{v}|^{2}=\vec{v}^{*} \cdot \vec{v}=\sum_{i=1}^{\infty}\left|v_{i}\right|^{2}$$

## 物理代考

9.1 希尔伯特空间

$$\开始{对齐} \vec{v} &=\left(v_{1}, v_{2}, v_{3}\right) \ \vec{a} \cdot \vec{b} &=\sum_{i=1}^{3} a_{i} b_{i} \end{对齐}$$

• 扩展空间以拥有无限的维度；
• 让向量的分量变得复杂。
75
76 一个然后有
量子力学导论
然后向量长度的平方由下式给出
$$|\vec{v}|^{2}=\vec{v}^{*} \cdot \vec{v}=\sum_{i=1}^{\infty}\left|v_{i}\right |^{2}$$

Matlab代写