ph135_hw1 - -are eigenstates of s z (eg. s z + = 1 2 + and...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 135c H. W. Assignment 1 1.) Determine the order of energy levels for a very deep ( V 0 >> ¯ h 2 /ma 2 for r > a and V 0 = 0 for r a ) 3-dimensional potential. Draw an energy level diagram for the Frst 10 discrete levels, with the spacing between levels scaled according to the energy di±erences. Label the levels with the principal quantum number and the angular momentum of the state, using the notation where s, p, d, f, g, h ,... corresponds to l = 0,1,2,3,4,5. .. (eg. 1 s for n = 1 , l = 0 and 4 f for n = 4 , l = 3). Do the same calculation and draw a similar energy level diagram for the Frst 5 discrete energy levels for a 3-dimensional harmonic oscillator potential ( V = 2 r 2 / 2). In each case be sure to indicate any degeneracies, and include the number of identical fermions that can be placed in each level. 2.) Consider the following spin wave function for a particle with spin 1/2: φ spin = + + - , where χ + , χ
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: -are eigenstates of s z (eg. s z + = 1 2 + and s z -=-1 2 -). Determine the relation between the coecients a and b and the direction of the particles spin given by the spherical coordinates and . 3.) Construct all possible spin wave functions | JM > obtained from adding three spin 1/2 particles. Your Fnal wave functions should be expressed in terms of | m 1 m 2 m 3 > basis states using the notation | m 1 m 2 m 3 > = | >, | >, . .. Comment on the symmetry of these states under the particle exchange operator. 4.) Bertulani Problem 1.6 (Chap. 1, Prob. 6) 5.) Given that J = 1 + for the deuteron, that the pion has spin zero, and that the reaction -+ d n + n can be observed when the -is captured at rest, determine the parity of the -....
View Full Document

This note was uploaded on 12/04/2011 for the course PHY 7070 taught by Professor Smith during the Spring '11 term at Wisconsin.

Ask a homework question - tutors are online