Lecture 7 Notes Ehrenfest’s Theory

Lecture 7 Notes Ehrenfest’s Theory - Lecture 7 Notes...

Info icon This preview shows pages 1–2. Sign up to view the full content.

Lecture 7 Notes: Ehrenfest s Theory In the previous section we showed that the Hamiltonian function plays a major role in our understanding of quantum mechanics using it we could find both the eigenfunctions of the Hamiltonian and the time evolution of the system. What do we mean by when we say an object is symmetric? What we mean is that if we take the object perform a particular operation on it and then compare the result to the initial situation they are indistinguishable. When one speaks of a symmetry it is critical to state symmetric with respect to which operation. How do symmetries manifest themselves in equations? Let us suppose that your system is symmetric with respect to translations in x that would imply that any physical property could nothave an x dependence. In particular the energy would not have an explicit dependence on x thus: H x , p 0   dp p const x dt The momentum in this case is called a constant of motion. This illustrates a fundamental connection between symmetries and conserved quantities. In fact, every symmetry in a physical system implies an associated conserved quantity.
Image of page 1

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

Image of page 2
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