{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

385lec8 - PHYS 385 Lecture 8 Schrdinger equation with...

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

View Full Document Right Arrow Icon
PHYS 385 Lecture 8 - Schrödinger equation with interactions 8 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 8 - Schrödinger equation with interactions What's important : energy operator SE with potential energy Schrödinger equation in three dimensions Text : Gasiorowicz, Chaps. 3 Energy operator Recall again the form of the Schrödinger equation for a free particle in one dimension: i h ( x , t ) t = - h 2 2 m 2 ( x , t ) x 2 (1) In the previous lecture, we established that the momentum operator p op could be represented by p = - i h x (2) when operating on wavefunctions in position-space, ( x , t ). From now on, we drop the "op" subscript unless we need it for clarity. Squaring this (not complex square!), p 2 = - h 2 2 x 2 (3) which bears a resemblance to the right-hand side of Eq. (1). Substituting, (1) becomes i h ( x , t ) t = p 2 2 m ( x , t ) Now, p 2 / 2 m is just the non-relativistic kinetic energy, so the action of the right hand side is to operate on ( x , t ) with the kinetic energy operator. Note that we say "operate
Image of page 1

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

View Full Document Right Arrow Icon
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