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...
theres 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.
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...
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 independant
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...
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)...