This preview shows pages 1–2. 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: PHY6938 Proficieny Exam Fall 2002 September 13, 2002 Modern Physics and Quantum Mechanics
1. Consider a onedimensional step potential of the form V (x) = 0 x<0 V0 x 0 where V0 > 0. A particle with total energy E > V0 and mass m is incident on the step potential "from the left" (in other words: the particle starts at negative values of x and travels toward positive values of x). (a) Use the timeindependent Schrdinger equation to determine the form o of the particle's wave function in the two regions x < 0 and x 0. (b) Derive expressions for the probabilities that the particle is reflected (R) and transmitted (T ). Hint: Recall that the probability density current is given by j(x) = Re h , im x and that R and T are ratios of probability density currents. 2. The nucleus 113 Cd captures a thermal neutron having negligible kinetic energy, producing 114 Cd in an excited state. The excited state of 114 Cd decays to the ground state by emitting a photon. Find the energy of the photon. 3. A current of quantummechanical particles of mass m can be written as J = i h [  ] , 2m where is the wave function. Assume that the particles move through a region of space where the potential is complex V = Vr  iVi . Show that particles are being annihilated at a rate 2 R = Vi h per unit volume. Hint: Use the timedependent Schrdinger equation to obtain "the material o derivative" ( ) + J . t 4. Cosmic ray photons from space are bombarding your laboratory and smashing massive objects to pieces. Your detectors indicate that two fragments, each of mass m0 , depart such a collision moving at speed 0.6 c at angles of 60 relative to the photon's original direction of motion. (a) In terms of m0 and c, what is the energy of the cosmic ray photon ? (b) In terms of m0 , what is the mass M of the particle being struck (assumed to be initially stationary) ? ...
View
Full
Document
This note was uploaded on 03/11/2012 for the course PHY 3900 taught by Professor Staff during the Fall '1 term at FSU.
 Fall '1
 staff
 Energy, Mass

Click to edit the document details