Quantum State Transfer

In the Summer of 2023, I went to UC Davis COSMOS: Quantum Mechanics. One of my projects was to solve the time-independent Schrodinger's Equation, in the form of matrices! For those of you extra curious, I've left an algebraic explanation below! I then wrote code, using my solution to calculate the wave function, that simulates the probability of an electron being at any position in a given structure. I then carefully manipulated the Hamiltonian matrix in order to create "perfect" quantum state transfer, where the electron oscillates from the first to the last position with 100% certainty. See the animations below!

From top right to bottom left: Perfect Quantum State Transfer for a 1D chain of atoms, Normal Quantum State Transfer for a 1D chain of atoms, and the x value of Quantum State Transfer for a 2D hexagonal lattice.

Scanning Tunneling Microscope

These are images of my group's hand-built scanning tunneling microscope! My group was able to achieve electron tunneling and extrapolate that data to image the surface of graphite and gold samples! Without a vaccum and proper stabilization, our results had a lot of error, but it was a great experience!