Recent content by halfoflessthan5

okay got it. I put the operator into the RHS of the hermitian condition, took the complex conjugate and re-arranged it so that it was in the same form as the LHS of the hermitian condition. the inequality obviously doesn't hold because the 'i' put a minus in one, so the operator wasn't...

there's one line that keeps coming up in proofs that I don't get. How do i get from \int (\hat{p}\Psi1)*\Psi2 + i \int (\hat{x}\Psi1)\Psi2 to \int ( (\hat{p}-i\hat{x}) \Psi1)*\Psi2 using the fact that p and x are Hermitian. im sure its painfully simple but i can't see it.

yeh okay. that was obvious :redface: thankyou

bump anyone?

Homework Statement the equation of motion for a damped harmonic oscillator is d^2x/dt^2 + 2(gamma)dx/dt +[(omega0)^2]x =0 ... show that x(t) = Ae^(mt) + Be^(pt) where m= -(gamma) + [(gamma)^2 - (omega0)^2 ]^1/2 p =-(gamma) - [(gamma)^2 - (omega0)^2 ]^1/2 If x=x0 and...

Its not a normal integral youre doing, its like a 'partial integral.' I remember this confusing me too.

thankyouuu

Is this right then: (2i -2j)x + (3j - k)y + (i + 2j +k)z = 0 multiply out and rearrange (2x + z)i + (-2x + 3y +2 z)j + (z - y)k = 0 comparing is js and ks on each side 2x + z = 0 -2x + 3y + 2z = 0 z - y = 0 as matrices [2 0 1] [x] = [0] [-2 3 2] [y]...

just a quick one: Homework Statement Show that the vectors a=2i -2j, b=3j - k and c = i + 2j +k are linearly independent Homework Equations The Attempt at a Solution What does 'linearly independent' mean and what's the test for it? Its from a really old exam paper so i might...

yeh, okay. and when you change the dx to dt you get 1/cosx which cancels the one in the integrand. very clever thankyou Eighty , much appreciated

okay got it. So i can think of f(x,y) as like a contour map with a load of concentric circles each representing a value of f(x,y.) So you workout grad f(x,y) and normalize it then set (x^2 + y^2) to R^2... and it works! thankyou for all the help mystic. Youre a legend

sorry I am not sure i understand that. what is f'(x)dx=df(x)? (ive probably done that type of integration before but not with that name or notation. is that 'd' as in 'dx' or just a constant) and I am not sure what substitution "without a new named variable means" either :confused: your...

Yes! its R d(theta.) The length of the arc subtended. Which would provide the extra R. Excellent, thankyou :biggrin: Okay point taken. I am not sure how else to write the function though. f(x) = +/-(1 - x^2)^(1/2) would give the top and the bottom but i can't do anything with that. (just...

what is the quick way of doing single integrals of the form: *integral* (sinx)^n (cosx)^m dx where n and m are just integers. These kind of integrals come up all the time in vector calculus and they take me ages to do. Is there a general method of doing them or a few common integrals i...

Question Evaluate both sides of the divergence theorem for V =(x)i +(y)j over a circle of radius R Correct answer The answer should be 2(pi)(R^2) My Answer the divergence theorem is **integral** (V . n ) d(sigma) = **double intergral** DivV d(tau) in 2D. Where (sigma)...