ECE495N-F08-HW_4

# ECE495N-F08-HW_4 - ECE 495N Fall08 ME118 MWF 1130A 1220P...

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

9/10/08 ECE 495N, Fall’08 ME118, MWF 1130A – 1220P HW#4: Due Wednesday Oct.15 in class. Note: Problems 4 and 5 are carried over from HW#3 Problem 1: Consider the (2x2) matrix A = cos θ sin e i ϕ sin + cos Show that the following V 1 cos( /2) /2 sin( /2) + and 2 sin( /2) cos( /2) + are eigenvectors of [A]. What are the corresponding eigenvalues? Are they orthogonal (that is, is 1 + 2 = 0) ? Note: the superscript ‘+’ denotes Hermitian conjugate. Problem 2: Define a (2x2) matrix [ ] [{ 1 } { 2 }] Now calculate the matrix [B] = [V + ] [A] [V]. (A and [ ] [{ 1 } { 2 }] are given in Problem 1). Assuming ,0 2 π θϕ = , use MATLAB to find [V] and check that [B] = [V + ] [A] [V]. (HINT: use “[V, B]=eig(A)” command) Problem 3: Using the 2s and the three 2p levels as basis functions write down the Hamiltonian matrix for a hydrogen atom in an electric field F directed along the x-axis. Find the eigenvalues and eigenvectors. You may find Section 4.4.2 (page 99) of the text useful.

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

View Full Document
9/10/08
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/30/2010 for the course ECE 495N taught by Professor S.datta during the Spring '08 term at Indiana University-Purdue University Fort Wayne.

### Page1 / 2

ECE495N-F08-HW_4 - ECE 495N Fall08 ME118 MWF 1130A 1220P...

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

View Full Document
Ask a homework question - tutors are online