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: Physics 4120 Spring 2008 Homework #3 1) Reif 2.1 ( 29 E E m p p mE p δ δ + = + = 2 2 Shaded region is accessible to our particle. 2) Reif 2.2 Slice of phase space through position is simple. Slice of phase space through momentum forms a ring, with inner radius p and outer radius p+ δ p, where ( 29 E E m p p mE p δ δ + = + = 2 2 3) Reif 2.3 a) Total probability of being within the darkly shaded region is given by the probability density integrated over that interval. We can use either P(x) or w ( ϕ ) to do this, so the integrals must be equal. Note that we add a factor of 2 since when we integrate over dx , we’re automatically taking both the top and bottom half of the circle: ( 29 ( 29 ( 29 2 2 2 2 2 cos 1 sin cos 2 1 2 ) ( 2 ) ( 2 1 2 1 2 1 x A dx d d x A d t A d t A dx t A x d d w dx x P x x = = + = + = + = = = ∫ ∫ ∫ ϕ ϕ ϕ ϕ ϖ ϕ ϕ ϖ ϕ ϖ ϕ π ϕ ϕ ϕ ϕ ϕ ϕ Note the minus sign: we need that because we have to switch the direction we’re integrating. ∫ ∫ ∫ ∫ ∫ ∫ = = = = 2 1 2 1 1 2 2 1 2 1 2 1 2 2 2 2 2 2 ) ( 1 1 ) ( x x x x x x x A dx dx x P x A dx x A dx d dx x P π π π ϕ π ϕ ϕ ϕ ϕ ϕ ϕ Note the switch in integration order gets rid of our minus sign and aligns the integration...
View
Full
Document
This note was uploaded on 04/17/2008 for the course PHYS 4120 taught by Professor Vajk during the Spring '08 term at Missouri (Mizzou).
 Spring '08
 Vajk
 Thermodynamics, Momentum, Work

Click to edit the document details