Quantum Chemistry 39 Average Position

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Short lecture on the expectation value of position. • Physical properties are represented in quantum mechanics by linear, Hermitian operators. The expectation value (average value) of a physical property is the integral over all space of the complex conjugate of the wavefunction times the operator acting on the wavefunction. The average position of a particle in a box is the midpoint of the box. The average square position can be computed analogously. The variance in the position is the difference between the mean square value and the square of the mean value. The standard deviation (uncertainty) is the square root of the variance. • Notes Slide: http://i.imgur.com/VkkGMR3.png • -- About TMP Chem -- • All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. • Email: [email protected] • -- Video Links -- • Chapter Playlist: • Particle in a Box / Schrodinger Equation • Course Playlist: • Quantum Chemistry and Spectroscopy • Course Review: • Quantum Chemistry Chapter Reviews • Other Courses: • PChem Course Intros • Channel Info: • About TMP Chem • -- Social Links -- • Facebook: / tmpchem • Twitter: / tmpchem • LinkedIn: / tmpchem • Imgur: https://tmpchem.imgur.com • GitHub: https://www.github.com/tmpchem • -- Equipment -- • Microphone: Blue Yeti USB Microphone • Drawing Tablet: Wacom Intuos Pen and Touch Small • Drawing Program: Autodesk Sketchbook Express • Screen Capture: Corel Visual Studio Pro X8

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