Sunday, March 4, 2012

Bringing It All Together

One of the most enjoyable aspects of my advanced physical chemistry class this semester has been employing the knowledge learned in my math classes. After I graduate next spring, I will have degrees in math and chemistry, however I don’t plan to directly utilize my math degree. However, for the first time this semester, I am starting to see that a firm background in math will serve me well in the future.
Right now in my chemistry class we are studying quantum mechanics. From what we’ve learned so far, everything essentially comes down to solving the wave function, which is a mathematical expression that is used in order to predict where an electron may be at any instantaneous moment. The wave function is defined by (x), which is a second-order, linear differential equation:

I was really excited to apply my knowledge from Applied Differential Equations I, a course I took last semester (I’m currently enrolled in the second semester). One of the best aspects of this chemistry class is the size – it’s one other student, my professor, Dr. Bohorquez and me!
A few weeks ago, Dr. Bohorquez actually turned the tables on me. She knows that I am also a math major, and decided to let me teach the class (Kyle) how to solve the wave function. It was a fun class, and after an hour, Kyle knew how to solve some basic differential equations!
As we’ve progressed through the course material, we’ve come across other situations where advanced integration and substitution techniques need to be utilized in order to evaluate an integral or solve an equation. Essentially this chemistry class has been transformed into a math class for the time being!
Once the wave function has been solved, the mathematical solutions can be graphed in three dimensions to provide a visual model for the probability of finding an electron. The funky shapes of the orbitals are all expressed through mathematical formulas. Check them out below!

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