Taylor Larrechea

Physicist, Computer Scientist, Problem Solver

Physics

In May 2020, I had the privilege of graduating from Colorado Mesa University, where I was immersed in an intellectually stimulating environment that culminated in earning a Bachelor of Science in Physics, complemented by a minor in Mathematics. This period was marked not merely by academic pursuits but by a profound journey of discovery and growth. As a Physics undergraduate, I found myself at the nexus of complex theoretical concepts and practical applications, a position that allowed me to hone a versatile skill set. This journey was characterized by an extensive exploration of mathematical intricacies, fostering an ability to navigate and solve multifaceted problems with ease and precision. Beyond the realm of numbers and formulas, my education instilled in me a robust foundation in critical thinking, enabling me to approach challenges with a meticulous and analytical mindset. Moreover, this experience was enriched by developing a myriad of other skills, all of which are integral to the rigorous demands of the scientific field and beyond. These years were not just about acquiring knowledge; they were about shaping a mindset equipped to tackle the unknown, armed with curiosity, resilience, and a relentless pursuit of excellence.

During my quest of obtaining my B.S in Physics from CMU, I took a myriad of Math and Physics courses that shaped me into the critical thinker and problem solver that I am today. Below is a list of courses that I took that aided me in obtaining the expertise that I now have.

  • Calculus 1 – An introductory course into differential and integral Calculus.
  • Calculus 2 – An extension of Calculus 1 that dives into more complicated integration techniques, series, and other related Calculus topics.
  • Calculus 3 – A course that serves as a multivariate extension of both Calculus 1 and 2.
  • Differential Equations – An introductory course into techniques that are used to solve mathematical equations that describe the relationship between a function and its derivatives.
  • Fourier Analysis – A course focused on decomposing complex signals into simpler trigonometric functions.
  • Mathematical Modeling – A course focused on using mathematical techniques to model everyday phenomena.
  • Numerical Analysis – A course focused on the study of algorithms that use numerical approximations for the problems of mathematical analysis that cannot be solved analytically.
  • Methods Of Applied Mathematics 1 – A course focused on mathematical techniques that are used to solve complicated analytical problems.
  • Methods Of Applied Mathematics 2 – A course focused on mathematical techniques that are used to solve complicated numerical problems.
  • Introduction To Classical Mechanics – An introductory physics course focused on Newtonian laws, energy, and momentum.
  • Introduction To Electromagnetic Theory – An introductory physics course focused on interactions between electric charges encompassing electric and magnetic fields.
  • Intermediate Dynamics – A physics course focused on the study of thermodynamics, special relativity, and waves.
  • Electronics – A course focused on how circuits work.
  • Modern Physics – An introductory course focused on newly found fields in physics, primarily quantum mechanics.
  • Intermediate Lab – An introductory physics course focused on the experimental techniques that are used to test theories in physics.
  • Classical Mechanics – A physics course that focuses primarily on Lagrangian and Hamiltonian mechanics.
  • Electromagnetic Theory 1 – A physics course that serves as an extension of the introductory electromagnetic theory course.
  • Quantum Mechanics 1 – A physics course that describes the physical properties of nature at the scale of atoms and subatomic particles.
  • Statistical Mechanics – A physics course that describes the physical properties of nature at the macroscopic level.
  • General Relativity – A physics course that discusses the theory of gravitation as the consequence of the curvature of spacetime caused by mass and energy.
  • Advanced Lab – A continuation of the introductory physics course in experimental techniques that are used to test theories in physics.
  • Senior Seminar – A capstone course in physics that focuses on the communication of physics research.
  • Senior Research – A capstone course in physics focused on the techniques to perform research in the field of physics.

My work for this degree can be found at my CMU repository in my GitHub. Below is a link to my official transcript from CMU where I graduate with honors.

CMU Transcript

Experimental Projects

During my time pursuing my Physics degree from Colorado Mesa University, I complete numerous experimental projects. Below are the primary projects / experiments that I completed.

Atomic Spectroscopy Of A Hydrogen Spectrum

We aim to find the wavelengths of light produced by hydrogen as the source of the light as predicted by quantum theory. A spectroscope was used in this experiment to display the spectrum of light that was to be observed. The colors of light observed were red, green, and purple. Red was found to have a wavelength of 675.9 ± 1.8 nm where green had a wavelength of 498.9 ± 0.1 nm and purple had a wavelength of 445.3 ± 1.1 nm. The theoretical wavelength value for red light is 656.1 nm where as green and purple are 486.0 nm and 433.9 nm respectively.

Atomic Spectroscopy
Heat Capacity Of Water

The purpose of this lab is to determine the specific heat of water. The experimentally found value for the specific heat of water was found to be 4,000 ± 500 Jg−1 K−1. The accepted specific heat of water is 4, 184 J g−1 K−1.

Heat Capacity Of Water
Modeling The Equations Of Motion For Coupled Pendulums

The dynamics of two coupled pendulums is studied with the goal of solving for the equations of motion. The equations of motion that were solved in this experiment were modeled with Lagrangian Mechanics. Numerical methods were used to solve the equations of motion derived from Lagrangians in this experiment. The numerical solutions showed that the pendulums behaved in the same manner as the data that was recorded. Both experimental data and the numerical solution show that the pendulums eventually oscillate at the same frequency but out of phase of one another.

Modeling The Equations Of Motion For Coupled Pendulums
Period Vs. Amplitude Of A Simple Pendulum

We address the question of whether or not the period of a simple pendulum depends on it’s amplitude. Experimental tests were done to compare the period of a simple pendulum for two different amplitudes. It was concluded from this experiment that the period of a pendulum does depend on it’s amplitude. It was also found that the acceleration due to gravity in this lab was g = 9.77 ± 0.02m s−2 and was found by knowing the period of the pendulum and the length of the pendulums arm.

Period Vs. Amplitude Of A Simple Pendulum
Room Temperature Raman Spectrum Of Titanium Dioxide And Sulfur

Stokes and anti-Stokes intensities are reported along with the relative wavenumbers for Titanium dioxide and Sulfur. The relative wavenumbers for the anti-Stokes and Stokes intensities were measured to be close to the same value in magnitude. The ratios of anti-Stokes to Stokes intensities for Titanium dioxide was measured to be 0.208 ± 0.045 where as the Sulfur ratio was 0.420 ± 0.070. Along with the ratios of the anti-Stokes to Stokes intensities, the room temperature was measured with the data that was collected in this experiment. The most accurate temperature value that was measured with the use of the Titanium dioxide in this experiment was 380 ± 44 K. Standard room temperature is taken to be 293 Kelvin according to NIST. This discrepancy was deter- mined to be caused by systematic error.

Room Temperature Raman Spectrum Of Titanium Dioxide And Sulfur
X-Ray Diffraction Of Table Salt

Table salt and potassium chloride are examined via X-Ray Diffraction to determine the lattice spacing. The lattice spacing of the table salt and potassium chloride sample was calculated by measuring the angle of Diffraction from X-Rays. The experiment produced a lattice constant for table salt of a = 0.567(1) nm. The lattice constant for potassium chloride was found to be a = 0.524(3) nm

X-Ray Diffraction Of Table Salt

Theoretical Projects

Along with my experimental projects, I have also completed theoretical projects while pursuing my Physics degree. Below are the primary projects that I completed.

Dynamics Of A Triple Star System

This article reports the examinations of a three body star orbit. These orbits are impossible to solve analytically and require numerical methods for plotting the orbits of these stars. Precisely, python and a Forward Euler Difference Scheme (Or F.E.D.S for short) was used to solve for these stars’ equations of motion. After these solutions were found, it was observed that these three body orbits are primarily unstable with only specific initial conditions yielding stable orbits of the three stars.

Dynamics of a Triple Star System
Improving Quantum Parameter Estimation

Quantum parameter estimation is the method of which quantum mechanical systems are used as devices to measure physical parameters. The parameters that are being estimated arise in various physical processes. Estimation accuracy is quantified by variance, which is bound by Quantum Fisher Information which can be calculated from the state of the system. The Quantum Fisher Information depends on whether single or multiple particles are used as probes and whether their states are correlated or independent. Sometimes certain multiple particle states yield greater accuracy comparable to classical particle states. Noisy states can mean the initial state is not perfectly known. Estimation has been partially assessed when available particle states are noisy. When specific channels incorporate additional noise the Quantum Fisher Information typically decreases rather than when the channels leave the particles undisturbed. When multiple particles are introduced that undergo phase flips, it has been shown to be advantageous for certain strengths of phase flips whereas depolarizing channels seldomly yield a better estimation than that of other methods.

Improving Quantum Parameter Estimation