week1 - 1 1.1 Introduction/Series Why this course exists...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Introduction/Series 1.1 Why this course exists PHZ3113 was created in the early 1990s in the department of physics as part of a general revamping of the undergraduate physics curriculum. The perception of many faculty at that time was that more and more students were arriving at so-called ”majors” courses like statistical mechanics and quantum mechanics math- ematically unprepared to understand lectures and perform exercises. One generally recognized problem was what a physicists would refer to as an “impedance mis- match” (i.e., difficulty of transporting information, energy, current etc. through an interface between two media because of very different properties of these media) between the physics and mathematics curricula at UF. As at many universities, mathematics is generally taught from the point of view of a mathematician, i.e. with a view to the formal structure of the subject and emphasizing aspects of in- terest to majors who might be considering doing research in the field. Physicists teaching 15 years ago found that students had an appreciation for the beauty of mathematics, and could, under some circumstances, prove some elementary the- orems, but were hard pressed to integrate the function sin x , much less solve the differential equation for a damped harmonic oscillator. Thus PHZ3113 was cre- ated to teach students, not just from physics but other scientific or engineering disciplines as well, the nuts and bolts of performing mathematical operations of use to our field, so that when they encounter a Hamiltonian matrix in PHY4604 (Quantum mechanics), they will know in their gut what a matrix is, how to find its eigenvalues and eigenvectors, how to invert it, and take its Hermitian conjugate, not just be able to prove that the dual of a monomorphism is an epimorphism (aside: your instructor remembers this statement from his undergrad linear algebra course, but not what it means). At the same time, teaching this material gives us the opportunity to explore aspects of the relationship between physics and mathematics which go well beyond nuts and bolts. Mathematics is sometimes called the language of physics, but can also be thought of as an infrastructure, a sort of highway system which connects different branches of physics, enabling insights from one to be exported from one to another. Think of an example you already know: the remarkable set of conclusions which follow from Gauss’s law in electrostatics, which are rigorously analogous to those derived by Newton for the gravitational force. At the level of laboratory physics, gravity and electromagnetism are completely distinct physical phenomena, yet they are bound together by a common mathematical framework. The fields 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
associated with a mass and a charge both fall off with the inverse square of the distance: E grav = Gm r 2 E Coul = 1 4 π 0 q r 2 , (1) where q is the charge, m is the mass, and 1 / (4 π 0 and G are the universal constants of electrostatics and gravity, respectively. But for
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern