# 量子、统计和复合物理|PHYS3034/PHYS3935 Quantum, Statistical and Comp Phys代写 sydney代写

You will learn how to use computer-aided design (CAD) software to design 3D printable molecular models that convey intermolecular interactions like hydrogen-bonding. The models will incorporate movable (i.e., rotation, flexion) and magnetic design elements to represent the formation of dynamic/weak bonds, which will serve as a useful visualisation and communication tool for complex molecular structures. The designs will be printed remotely and students will be able to keep their printed designs.

is also a nonnegative-definite Hermitian matrix, and we obtain the matrix inequality
$$\sum_{j=1}^{m}\left(x_{j}^{2}+y_{j}^{2}\right) M_{j} \geq X^{2}+Y^{2} \pm i[X, Y]$$
Since $S=S^{*}>0$ from the assumption, the above formula results in
$$\sum_{j=1}^{m}\left(x_{j}^{2}+y_{j}^{2}\right) S^{\frac{1}{2}} M_{j} S^{\frac{1}{2}} \geq S^{\frac{1}{2}}\left(X^{2}+Y^{2}\right) S^{\frac{1}{2}} \pm i S^{\frac{1}{2}}[X, Y] S^{\frac{1}{2}}$$

If $[X, Y]=0$, then $\Gamma(X, Y ; S)=\operatorname{Tr}\left[S\left(X^{2}+Y^{2}\right)\right]$ holds. In this case, if we define $M=\left{M_{j} ; x_{j} ; y_{j}\right}$ by (4)-(6), then (1) and (2) obviously hold and
$$\sum_{j=1}^{m} x_{j}^{2} M_{j}=X^{2}, \quad \sum_{j=1}^{m} y_{j}^{2} M_{j}=Y^{2}$$
hold, so that we have $\Delta(M ; S)=\operatorname{Tr}\left[S\left(X^{2}+Y^{2}\right)\right]$. Therefore, it gives the minimum of $\Delta$ and $\Delta_{*}(X, Y ; S)=\Gamma(X, Y ; S)$ holds.

## PHYS3034/PHYS3935 COURSE NOTES ：

$$\frac{1}{2 \pi \mu} \int(x+i y) E_{x, y} d x d y=X+i Y,$$
which can be also written as
$$\frac{1}{2 \pi \mu} \int x E_{x, y} d x d y=X, \quad \frac{1}{2 \pi \mu} \int y E_{x, y} d x d y=Y .$$
Moreover, if we multiply $X-i Y$ from the right in both sides, from $[X, Y]=i \mu I$, we have
$$\frac{1}{2 \pi \mu} \int\left(x^{2}+y^{2}\right) E_{x, y} d x d y=X^{2}+Y^{2}+\mu I .$$