This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Announcements Office hour: today 1-3pm. Last chance to go over Exam 2! New help room hour: Wednesdays 4-5 (see course web page for schedule (see course web-page for schedule) Reading for Friday: 7.4 - 7.5 HW 8 due on Friday noon.- h 2 2 m 2 ( x , t ) x 2 + V ( x , t ) ( x , t ) = i h ( x , t ) t The Schrodinger Equation Once at the end of a colloquium Felix Bloch heard Debye saying something like: Schrdinger, you are not working right now on very important problemswhy dont you tell us some time about that thesis of deBroglie, which seems to have attracted some attention? So, in one of the next colloquia, Schrdinger gave a beautifully clear account of how deBroglie associated a wave with a particle, and how he could obtain the quantization rulesby demanding that an integer number of waves should be fitted along a stationary orbit. When he had finished, Debye casually remarked that he thought this way of talking was rather childishTo deal properly with waves, one had to have a wave equation. Review: Superposition of plane waves 3 Plane Waves vs. Wave Packets Plane Wave: (x,t) = Aexp( i ( kx- t )) Wave Packet: (x,t) = n A n exp( i ( k n x- n t )) Q1 A. p most well-defined for plane wave, x most well-defined for wave packet. B. x most well-defined for plane wave, p most well-defined for wave packet. C. p most well-defined for plane wave, x equally well-defined for both. D. x most well-defined for wave packet, p most well-defined for both. E. p and x equally well- defined for both. For which type of wave are position x and momentum p most well-defined? Plane Waves vs. Wave Packets Plane Wave: (x,t) = Aexp( i ( kx- t )) Wavelength, momentum, energy well-defined. Position not well-defined: Amplitude is equal everywhere, so particle could be anywhere! Wave Packet: (x,t) = n A n exp( i ( k n x- n t )) , p, E not well-defined: made up of a bunch of different waves, each with a different ,p,E x much better defined: amplitude only non-zero in small region of space, so particle can only be found there. Heisenberg Uncertainty Principle In math: xp h /2 (or better: xp x h /2) In words: Position and momentum cannot both be determined completely precisely. The more precisely one is determined, the less precisely the other is determined. Should really be called Heisenberg Indeterminacy Principle. This is weird if you think about particles, not very weird if you think about waves. Heisenberg Uncertainty Principle x small p only one wavelength x large p wave packet made of lots of waves x medium p wave packet made of several waves A slightly different scenario: y Plane-wave propagating in x-direction....
View Full Document