CHEM 452 Lecture Notes - Lecture 4: Uncertainty Principle, Free Particle, Materials Science
Document Summary
Review from lecture 3: heisenberg uncertainty principle, limit on knowledge of, position and momentum, energy and time, general form described by commutator of operators, operator on a general function to find uncertainty in knowledge of x and p. [ ,(cid:1868) ](cid:1858)(cid:4666)(cid:4667)= (cid:1858)(cid:4666)(cid:4667) therefore, commutator has value : uncertainty in = = (cid:1731)(cid:2870)(cid:1732) (cid:1731)(cid:1732)(cid:2870, (cid:1868)= (cid:1731)(cid:1868)(cid:2870)(cid:1732) (cid:1731)(cid:1868)(cid:1732)(cid:2870) it can be shown that x p=(cid:2869)(cid:2870)| ,(cid:1868) | from which we get (cid:1868)= (cid:2870) Defining k: predicts exactly wavelength that debroglie postulated (cid:4666) d=h/p, plus, or minus because you don"t know the direction the particle is going in, e-v= ke. Physical system: = (cid:2870, =(cid:1827)(cid:1857)+(cid:1828)(cid:1857) if b=(cid:882),k= (cid:2870)(cid:3040) 2(cid:4666)(cid:1831) (cid:4667, describes a free particle moving in +x direction with momentum, (cid:1863, no limit to knowledge of k, born interpretation of . | (cid:2870)|= =((cid:1827)(cid:1857) )((cid:1827)(cid:1857))=(cid:1827)(cid:2870: heisenberg uncertainty principle, constant for all x, no knowledge of x.
