Recent content by J.D.

In the case of spin, use the fact the spin functions only act on states alpha and beta. I.e. write out the determinant, which for a 2x2 matrix is ad-bc, act on \psi (1,2) with \hat{S}_{z,total} and then see if you get back an eigenvalue equation. Also remember that S_{z,1}, S_{z,2} only...

I would start by "simplifying" the R.H. side and then compare it to the L.H. side. Thus: A(x+2)(x-2)+Bx(x-2)+Cx(x+2) = Ax^2 -4A +Bx^2 - 2Bx +Cx^2+2Cx = \dots = x^2+4x-2

Actually I am a little uncertain here if I should calculate either \frac{\partial ^2 \delta ( x' - x'')}{\partial x''^2} or \frac{\partial ^2}{\partial x''^2} \left( \delta ( x' - x'') \text{e}^{-\beta x''}\right) in I_1 .

Shouldn't you consider the expanded eigenkets? | n > = |n^{(0)}>+\lambda |n^{(1)}> + \lambda^2 |n^{(2)}> + \dots Then you get to first order something like: <x> = < n^{(0)} | x | n^{(0)} > + \lambda \left( < n^{(0)} | x | n^{(1)} > + < n^{(1)} | x | n^{(0)} > \right)+ \mathcal{O}...

Homework Statement Solving a problem about the variational method I came across one nasty integral. Here goes: \bar{H} := \frac{ < \hat{0} | H | \hat{0} > }{< \hat{0} | \hat{0} >} Homework Equations H = -\frac{ \hbar^2 }{2m} \frac{\partial ^2}{\partial x^2} + \frac{1}{2} m...

Ok, I think I've finally come up with an acceptable solution. Here goes. We know that we can write an infinitesimal rotation R ( d \theta ) as R ( d \theta ) = 1 + i \mathbf{J} \cdot \hat{ \mathbf{n} } d \theta . (1) We also know that if R is an operator generating equations it must...

I think what you mean is: Given \frac{d^2 x}{dt^2} = 2 , \quad \forall t \geq 0 and \frac{dx}{dt}(0) = -5 and x(0) = 4 . You will then find that c is not -2.5. And I now see that neutrino already told you that...

If you have a function f(y) = y + 1 then the meaning of f \left( \frac{1}{2} (x+2) \right) is f(y) when y = \frac{1}{2} (x+2) and thus f( y = \frac{1}{2} (x+2) ) = \frac{1}{2} (x+2) + 1

That also makes sense. I really feel that there is something wrong with the original question and have my doubts whether or not there even exist a solution. I have to admit though that I haven't made any serious attempts to prove it.

Sure it shouldn't say a+b+c=90? Because then we could use tan(30^{\circ}) = \frac{\sqrt{3}}{3} and get the correct result.

Ok, so I've gone over this problem like a hundred times and finally settled for an approach to the problem. From what I gather it is most simple to look at an infinitesimal rotation, we know that we can write an infinitesimal rotation as: \mathcal{D} ( d \theta ) = \left( 1 + i \mathbf{J}...

It would seem that they are interested in knowing if the image is real or imaginary and if it's larger or smaller than the object in question.

If it helps, remember that \int^{b}_{a} x^n dx = { \left[ \frac{x^{n+1}}{n} \right] }^b_a . And as mda said, it would be helpful to know how your calculations look.

[SOLVED] Sakurai Ch.3 Pr.6 Homework Statement Let U = \text{e}^{i G_3 \alpha} \text{e}^{i G_2 \beta} \text{e}^{i G_3 \gamma}, where ( \alpha , \beta , \gamma ) are the Eulerian angles. In order that U represent a rotation ( \alpha , \beta , \gamma ) , what are the commutation rules...