Recent content by yukawa

Show that [A,B] = AB - BA = iqI, where q is a real no. and I is the identity matrix, cannot be satisfied by any finite dimensional Hermitian matrix A and B. I think this problem is something related to the uncertainity relation: <(\Delta A)^{2}><(\Delta B)^{2}>\geq \frac{\left|C\right|...

Homework Statement Show that 1/(A-B) = (1/A) + (1/A)B(1/A) + (1/A)B(1/A)B(1/A) + (1/A)B(1/A)B(1/A)B(1/A)+... where A and B are matrices whose inverse exist. The Attempt at a Solution I tried to start from the LHS by pulling out (1/A): LHS = (1/A)[1 + B(1/A) + B(1/A)B(1/A) +...

Oh! yes! I got it. Thank you very much.:smile:

the eigenvectors(left) and eigenvalues(right) of the Hamiltonian are: \left|\uparrow\uparrow\right\rangle : (1+c)/2 \left|\downarrow\downarrow\right\rangle : (1+c)/2 \frac{1}{\sqrt{2}}(\left|\uparrow\downarrow\right\rangle - \left|\downarrow\uparrow\right\rangle ) : (-3+c)/2...

I tried to find it by using this formula: \rho = \frac{e^{-\beta H}}{Z} where \beta = \frac{1}{kT} and \ Z = tr (e^{-\beta H}) I was stuck at finding \ e^{-\beta H} . The following is what i tried in order to find \ e^{-\beta H} . i) finding the eigenvectors and eigenvalues of H...

How to obtain the density matrix of the following system at thermal equilibrium? Given: Hamiltonian H :(in 4x4 matrix form) Hij = the i-th row and j-th column element of H H11 = (1+c)/2 H22 = -(1+c)/2 H23 = 1-c H32 = 1-c H33 = -(1+c)/2 H44 = (1+c)/2 where c is a parameter and all...

Is the following correct? BC: partial(x)/partial(u)= 0 at x=0 and x= l IC: u(x,0) = 2(epsilon)l , partial(u)/partial(t)=0 at t=0

Finding the vibrational motion of a rod. A uniform rod of length l is compressed from both ends so that its new length becomes l(1-2 \epsilon). The compression force is then removed and the rod is left to vibrate freely. Find the subsequent vibrational motion of the rod. What are the...

but are these two angles independent of each other? (in fact, i don't know how to determine whether two coordinates are independent of each other or not)

Lagrange equation of motion (from Marion 7-7) A double pendulum consists of two simpe pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lenghts and have bobs of equal mass and if both pendula are confirned to move in the same plane, find...