Recent content by rogeralms

You are correct. I wrote down the third eigenvalue incorrectly. It is correct on the attachment but the matrix is incorrect. The third eigenvalue should be ε3=ε0+2V0 The third matrix should be -2V0 V0 V0 V0 -2V0 V0 |χ1> = 0 V0 V0 -2V0

I took the solutions for the eigenvalues from part b (two of which are degenerate) and subtracted them from the Hamiltonian matrix. These are supposed to be the eigenvalue equations where the chi's should be the eigenvectors.

Consider a triatomic molecule with three identical atoms that are bound together with each atom at its own corner of an equilateral triangle of edge length a. An added electron on the molecule can be put in an identical atomic orbital on any of the three atoms. Denote the atomic states in which...

I overlooked the part in the problem statement that said that A and B both commute. Then we have Assume [A,Bn]=nBn-1[A,B] is true Show that it is true for n+1 [A,Bn+1]=(n+1)Bn[A,B] is true. [A,Bn+1]=[A,BnB]=Bn[A,B]+[A,Bn]B=Bn[A,B]+B[A,Bn] =Bn[A,B]+BnBn-1[A,B]=Bn[A,B]+nBn[A,B]=(n+1)Bn[A,B]

Thank you but I know how induction works. That is why I set up the problem with n+1. I need a hint on how to manipulate the commutators to show this is true, that [A,Bn+1]=(n+1)Bn [A,B].

Homework Statement Let A and B be two observables that both commute with their commutator [A,B]. a) Show, e.g., by induction, that [A,Bn]=nBn-1 [A,B].The Attempt at a Solution Prove for n=1 [A,B1]=1B1-1 [A,B]. [A,B]=B0[A,B]=[A,B] Show that it is true for n+1 [A,Bn+1]=[A,BnB]=Bn[A,B]+[A,Bn]B...

Thank you. I see my mistake that the alpha must be kept separate. Then the result reduces to a real function.

Homework Statement Break integral into positive and negative, integrate, recombine and simplify and show that it reduces to a real-valued function. (See attachments) Homework Equations See attachments The Attempt at a Solution My solution is not reducing to a real-valued function. Please see...

Thanks for your response. It turned out I was so confused that I did not state the questions correctly. Please see attachment for answers which will clear up the confused questions.

Homework Statement The difference between the Euler and Lagrange equations and when to use each. How to set up Lagrange when the energies are non-holonomic such as friction. What is the difference between curly delta and plain derivative, eg Hamilton's equation Homework Equations Euler's...

Homework Statement Determine the Fourier Transform of the function shown. Plot the result using excel, MathCad, or Matlab. See attachment for figure of triangle above x-axis from -X0/2 tp X0/2 with a max height of 1 at x=0. Homework Equations The answer is F(k) = X0/2 [sin(kX0/4) /...

Thanks I finally understand part a) k=3i+5j+6z so unit k vector = k/(70)^(1/2) E(t) = E0 cos(k(dot)r - ωt) E(t) = 10 V/m * cos ( (3x + 5y + 6z)/ 70(1/2) - ωt) part d) k(dot)<x,y,z> = 0 then 3x + 5y + 6z = 0. So choose y = 0 gives 3x + 6z = 0. This makes x = -2z, so choose z...

Simon, Thank you so much for answering and sorry for the double use of k. That was the convention used in my textbook and in my professor's lectures. E(r,t) = E0 cos(\omega (t - r/c) + \epsilon) where k = ω / c Since cos varies between -1 and 1 and the amplitude is given as 10 V/m...

Homework Statement Consider a harmonic, electromagnetic plane wave traveling along a line from the origin to the point (3,5,6). It is linearly polarized and its electric field lies in a plane perpendicular to the direction of travel of the wave. The wavelength of the wave is 2.0mm and it has a...

Answer to pencil problem Attached is the answer for your falling pencil pleasure. Hope this helps someone.