Quantum Mechanics Homework: Uncertainty, Probability, and Stationary States, Slides of Quantum Mechanics

Download Quantum Mechanics Homework: Uncertainty, Probability, and Stationary States and more Slides Quantum Mechanics in PDF only on Docsity! • Today Sep 9 7pm: HW # 3 Pb 1.9, 1.14, 2.1, 2.2 •Tuesday Sep 13 by 7pm: HW # 4 Pb 2.4, 2.5, 2.7, 2.8 • Thursday Sep 15 by 7pm: HW # 5 Pb 2.10, 2.11, 2.12, 2.13, 2.14 Announcements Quantum mechanics Homework docsity.com No student assigned to the following transmitters: Announcements Quantum mechanics Please register your i-clicker at the class website! 1413C9CE 160C968C 92C4F6A A8E55D1 14AF1DA6 1E59FDBA docsity.com Uncertainty principle Quantum mechanics Ch 1.6 Pb 1.9 How to check the uncertainty principle? • Calculate and x 2x x • Calculate and p 2p p • Estimate the product x p • Compare to 2 docsity.com Quantum mechanics Ch 1 Probability current Pb 1.14 Density of probability 2 ( , ) ( , ) *x t x t     Probability between two points ( , ) b ab a P x t dx   , ( , )ab dP J a t J b t dt   where   * , * 2 i J a t m x x           docsity.com Quantum mechanics Ch 2.1 Time-independent Schrödinger equation 2 2 22 i V t m x          In general ( , )V x t Here function of x only The potential is independent of time ( )V x General solution: ( , ) ( ) ( )x t x t   “Stationary state” docsity.com Quantum mechanics Ch 2.1 Time-independent Schrödinger equation Solution (x) depends on the potential function V(x). • Space dependent part: 2 2 2 1 2 d V E m dx      2 2 2 ( ) 2 d V x E m dx      Global solution: /( , ) ( ) iEtx t x e   Stationary state docsity.com Quiz 3b “If the particle is in one stationary state, its expectation value for position is not changing in time.” A. True B. False Quantum mechanics docsity.com Quantum mechanics Ch 2.1 Stationary states Properties: • Expectation values are not changing in time (“stationary”): /( , ) ( ) iEtx t x e  * ( , )Q Q x dx i x      with * ( , )Q Q x dx i x      Q is independent of time 0 d x p m v m dt    The expectation value for the momentum is always zero In a stationary state! p(Side note: does not mean that and x are zero!) docsity.com