374chw11 - HW#11 Phys374Spring 2008 Prof. Ted Jacobson Due...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: HW#11 Phys374Spring 2008 Prof. Ted Jacobson Due before 5pm, Tuesday, May 13, 2008 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374c/ jacobson@physics.umd.edu 1. Evaluate R b a ( x 2- 3) dx for (i) [ a,b ] = [- 1 , 1], (ii) [ a,b ] = [0 , 2], (iii) [ a,b ] = [- 2 , 0], (ii) [ a,b ] = [- 2 , 2]. (See Chapter 14 for Dirac delta functions. Section 14.3 discusses delta function of a function, which was also explained in class.) 2. Consider the integral I = Z Z f ( x,y ) ( x 2 + y 2- R 2 ) (( x- a ) 2 + y 2- R 2 ) dxdy, taken over the entire xy plane. (a) Make sketches in the ( x,y ) plane showing geometrically where the two delta functions in in the integrand are non-zero, for a/R = 0 , 1 , 2 , 3. (b) Evaluate I . ( Suggestion : First do the y integral, using the first delta function to identify the relevant y values.) (c) Explain the qualitative behavior the dependence of I on a/R in terms of your sketch in part 2a. In particular explain why it diverges where it diverges, and where it is zero. ( Guidance : Imagine the delta functions as having a small width, before taking the limit as the width goes to zero and the height to infinity, so each of their regions of nonzero support forms a ring. Consider how the area of the region in which both delta functions are non-zero depends on a/R . The idea behind this was explained in class.) 3. Wavepackets and group velocity for a relativistic quantum particle In relativistic quantum mechanics, the (complex) wave function for a spinless par- ticle of mass m satisfies the partial differential equation 2 t = c 2 2 x - ( m 2 c 4 / h 2 ) , (1) where c is the speed of light and h is Plancks constant. This is called the Klein- Gordon equation. For simplicity it is assumed here that the wave function depends on only one space coordinate...
View Full Document

Page1 / 3

374chw11 - HW#11 Phys374Spring 2008 Prof. Ted Jacobson Due...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online