# Overview

This course offers a modern and accessible introduction to the laws of Quantum Mechanics and their use in the developing field of quantum technologies. The advancement of nanotechnology has enabled the creation of devices on an atomic scale, where the principles of Quantum Mechanics become crucial.  The course utilizes a matrix-based approach and allows students to use computer simulations to comprehend complex quantum devices. The primary objectives of the course include: understanding and describing the behavior of quantum systems and devices, recognizing the potential of quantum phenomena in revolutionary systems such as quantum computers, quantum-enhanced sensors, and secure quantum communication channels, and gaining the background knowledge needed to comprehend the functioning of current quantum technology. The prerequisites for the course are minimal and provide a foundation for more advanced study in the theory and application of Quantum Mechanics.

# Concepts

These concepts are studied through course content, mainly lecture notes and course recommended textbooks. Please note, unless referenced from another source, please assume the following information presented is interpreted, studied, and re-expressed from the course content. Furthermore, please refer to the course content directly, e.g. ask the lecturer or read the textbook, for the most relevant knowledge required for the course.

## Quantum Mechanics

### Fundamentals

#### History

##### Photoelectric Effect

The photoelectric effect was discovered by Heinrich Hertz in 1887 when he observed that light changes the voltage required for sparking to occur between two charged metal electrodes.

##### Planck-Einstein Relation

The photoelectric effect can be explained using the Planck-Einstein relation. The Planck-Einstein relation states that the photon energy, $$E$$ , is proportional to its frequency, $$\nu$$ . This relationship is mathematically respresented below:

Frequency:
$E=\hbar\omega$ $\mathrm{p}=\hbar\mathrm{k}$

or Angular Frequency:
$E=h\nu$ $\mathrm{p}=\frac{h}{\mathrm{\lambda}}$

where $$h\approx6.626\times10^{-34}\ \mathrm{J.s}$$ (shortened value) and $$\hbar=\frac{h}{2\pi}\approx1.054\times10^{-34}\ \mathrm{J.s.rad^{-1}}$$ which is the "reduced" Plank constant. The main idea behind this relationship is that a photon is a discrete packet of energy. However, at the same time, light is also an electromagnetic wave.

##### Wave Function
###### Wave Equation
\begin{equation} \mathrm{E}(\mathrm{r},t)=Ae^{i(\mathrm{k}\mathrm{r}-\omega t)} \end{equation}

#### Uncertainty Principle

The Heisenberg's uncertainty principle is defined as:
\begin{equation} \sigma_x\sigma_p\geq\frac{\hbar}{2} \end{equation}
where $$\sigma_{x,p}$$ is the position's, $$x$$ , and momentum's, $$p$$ , standard deviation respectively. And where $$\hbar$$ is Plank's constant.

The mathematical equation arise from the fundamental limitation to the variances of a particle's position and momentum that can be simultaneously measured. In PHYS1231 - Higher Physics 1B , the uncertainty principle has been defined as "fundamentally impossible to make simultaneous measurements of a particle’s position and momentum with infinite accuracy."

# Recommended Resources

## Course Recommended

### Textbook

• Claude Cohen-Tannoudji, Bernard Diu & Frank Laloe. Quantum Mechanics. Edn. 1 Vol. 1 (Wiley, 1991).
• Supriyo Datta. Quantum Transport: Atom to Transistor. Edn. 2 (Cambridge University Press, 2005).
• David A. B. Miller. Quantum mechanics for scientists and engineers. Edn. 1 (Cambridge University Press, 2008).
• Dennis M. Sullivan. Quantum mechanics for electrical engineers. Edn. 1 (IEEE Press, 2012)
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Created by Leon Luo on 2022/11/08 22:30

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