Cluster 1 -- Quantum Mechanics and Applications to Nanotechnology


Is it a particle? Is it a wave? It's both!  Electrons, normally considered particles, can instead behave as waves when they are scattered by an ordered array of atoms in a crystal. Similarly, the photoelectric effect can only be explained if the electromagnetic waves which describe light behaves like particles called photons. Quantum mechanics explains this dichotomy and thereby provides the fundamental description of the perplexing fashion in which matter behaves at very short distances.  Hence, quantum mechanics contains the principles needed to understand fields from solid-state physics to electronics and biology by explaining properties of atoms, chemical bonds, and how the periodic table of elements works. In the first part of the cluster, students will learn some of the basic theoretical principles and how to solve basic quantum mechanical problems computationally, laying the foundation for interpreting the experiments in the second part of the cluster.

Core Courses

Computations of Quantum Phenomena

The basic equations of quantum mechanics involve quite sophisticated mathematics. Fortunately, they can also be solved with some fairly simple computer programs. This portion of the cluster will begin with an introduction to the elements of programming in C which are needed to do quantum mechanics on a computer. (No previous programming experience will be assumed.)  By the end of the month, each student will write programs that illustrate how an electron's location involves a probability of being at a range of positions, rather than a precise value. Using the computer, students will calculate the spreading of the range of positions as time passes and how a quantum particle can `split up' so that there is a chance both for it to be reflected by, and to tunnel through, a barrier.  Time permitting, we will discuss how to achieve `perfect quantum state transfer’ in which a particle moves from one location to another without spreading, a key requirement for quantum computing.  Students can bring and use their own laptops (we will help you install a C compiler) or use one issued by COSMOS.

Quantum Physics Experiments and Applications to Nanotechnology

Each student will learn basic electronics to do quantum physics experiments. Students will use modern scientific instruments to measure the speed of electromagnetic pulses on a cable and also the energies corresponding to the band gaps for light-emitting diodes (LEDs) of different colors. (The inventors of blue LEDs won the 2014 Nobel Prize in Physics.) For the final project, small groups of students will work together to construct several scanning tunneling microscopes (STMs). An STM is an instrument that uses quantum mechanical tunneling to make images of individual atoms on the surface of a conducting solid.

Students will use a small computer programming in C to control their experimental apparatus in real-time. In addition, quantum mechanical ideas will be used to explain phenomena such as properties of crystalline solids, how lasers work, and how to detect single photons. A demonstration will show that double-slit interference of visible light continues to occur even when the flux of photons decreases to the single-photon level in a light-tight tube. Several distinguished faculty will give guest lectures connecting quantum mechanical ideas to their current research on nanotechnology and nanomaterials.