final - Physics 2D Spring 2010 Final Exam Friday June 11...

Info iconThis preview shows pages 1–3. 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: Physics 2D Spring 2010 Final Exam Friday June 11 11:30am to 2:30pm [Note: This is a closed-book exam; total score of this exam is 100 points.] Some possibly useful equations and relations: relativistic energy-momentum relation: E 2 = p 2 c 2 + ( m c 2 ) 2 where m is the rest mass Einsteins photon theory: E = hf deBroglies relation for matter wave: = h/p or f = E/h k = 2 / , = 2 f , c = f = /k , h = h/ (2 ) uncertainty principle: x p h 2 time-indepdent Schr odinger equation:- h 2 2 m 2 + U ( ~ r ) ( ~ r ) = E ( ~ r ) trignometric relations: sin( ) = 0 for = 0 , , 2 , 3 ,... cos( ) = 0 for = / 2 , 3 / 2 , 5 / 2 ,... sin(- ) =- sin( ), cos(- ) = cos( ) d d sin( ) =- cos( ), d d cos( ) =- sin( ) 1 1. Particle decay. [10 points] A particle of mass M , initially at rest in the lab frame, decays into a particle of smaller mass m which moves with speed u in one direction, and a (massless) photon which moves with speed c in the opposite direction. Find u in unit of c for m = M/ 2. What fraction of the initial energy is carried away by the photon? [Hint: Start with the conservation of total energy and momentum. You will need to make use of the energy-momentum relation for a massless particle.] 2. One-dimensional square well. [10 points] A particle of mass m is trapped in a square potential well of width a , i.e., with U ( x ) = 0 for < x < a , and U ( x ) = U > 0 elsewhere. (a) Use Heisenbergs uncertainty principle to estimate the zero-point energy of the particle in an infinite potential well, i.e., with U ....
View Full Document

This note was uploaded on 09/13/2010 for the course PHYS phys 2d taught by Professor Hirsch during the Spring '08 term at UCSD.

Page1 / 4

final - Physics 2D Spring 2010 Final Exam Friday June 11...

This preview shows document pages 1 - 3. Sign up to view the full document.

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