Updated to electronic spectroscopies.
Interaction of
molecules with radiation
n
i
n
j
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Three types of interactions
Absorption
Stimulated emission
Spontaneous emission
Depending on situations, the rate of one process may
dominate.
...
Essential Thermodynamics - summary of Cambridge IA chemistry TD
course.
Laws
First Law:
\[
dU =\delta q+ \delta w \label{td1}\tag{1}
\]
Second Law: entropy of the Universe increases in a
spontaneous process.
Entropy is classically defined as
\[
dS=\frac{\delta q_{rev}}{T}. \tag{2}\label{entro...
让对滑雪完全无感的我，回到全法最大滑雪度假村Val Thoren的唯一动力。
The motivation for a ski-phobia like me to return to Val Thoren.
参与牛剑Varsity
trip前往法国享受的一次滑雪之旅已经过去半年多了，而这家餐厅的记忆也自然而然随时间开始淡去。
“不行，不能忘，必须记录下来！”它给我带来的体验就是有这么优越。
于是，在这不尴不尬的时间点，胡编了一个“之最”的名号来赞美它。不想说得太绝对，毕竟我也没去过足够多的优秀餐厅。“学年最佳”，就一点也不假，完全可以甩心中的第二名13条街。
在短短的一周时间中，我们...
Cambridge IB Chemistry course with some IB Physics blended in.
Ionic Model
In the lattice, ions experience the force from neighbours,
next-neighbours, next-next-neighbours, …, forming a conditionally
convergent series.
The sum is (or rather from experimental data is deduced to be)
Madelung cons...
This is a only a summary of knowledge.
Fourier transform
There are many conventions as in where to put the normalisation \(2\pi\) factor.
Forward Fourier transform (Fourier analysis)
\[
\tilde{f}(k)=\int_{-\infty}^\infty f(x)e^{-ikx}\,dx
\]
Inverse Fourier transform (Fourier synthesis)
\[
f...
Functionals
Just like functions take variables as arguments,
functionals take functions as arguments.
In the following sections, the functional of the form
\[
G[y]=\int_\alpha^\beta f(y,y' ; x) \, dx
\]
is considered.
Functional derivatives
Definition:
\[\begin{align}
\delta G &= G[y+\de...
Key concepts
Linear operator
Homogeneous:
equation: no forcing, or, a multiple of a solution \(y\), \(\alpha
y\) is also a solution.
problem: in addition, \(\alpha
y\) also satisfies B.C.
Boundary conditions
Dirichlet: the function value on the boundary is defined
Neumann: the normal derivati...
Matrices
Vector space
Definition
A set of elements on which vector addition and
scalar multiplication are defined
Closed under these operations
Includes identity \(\mathbf{0}\)
for vector addition
Note:
2D spaces \(\mathbb{R}^2 \neq
\mathbb{C}\), since \(\mathbb{C}\) has a single point of \(\...
Contour Integration
Idea: A powerful method of doing integrals by using the properties of
complex functions.
Analytic functions
To be differentiable at a point, a function must satisfy
Cauchy-Riemann.
\[
\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y},
\,\frac{\partial v}{\partial...
Overall picture
Scale
Type
Energy scale / \(\pu{cm-1}\)
EM wave
Electronic
10000
UV/VIS, X-ray
Vibration
1000
IR
Rotation
1
Microwave
Requirements
Rotation (Microwave) Spectra
Need permanent dipole
x, y or z transforms as totally symmetric representation
Infrared
Need change in ...
