This is a Hamilton-Jacobi problem.
Homework Statement
A particle (mass m=1) moving on a line is attached to a light spring (length d, another end attached to the origin). The potential is:
V(q)=\left\lbrace \begin{array}{cc} \frac{1}{2}\omega^2 _0(|q|-d)^2 & when |q|\geq d \\ 0 & when |q|<d...
Yes, right.
I tried that but got a result that didn't solve the equation so I thought that my approach was wrong.
I tried it once again and this time got a result that works.
Ok, I've got it.
Thanks!
Thanks for your answers.
But I still don't get it for Z167:
x²+x+41=167
x²+x-126=0
x=\frac{-1\pm\sqrt{1-4\cdot 1\cdot(-126)}}{2}
The only way I get a reasonable result from that is if (under the square root):
1-4*1*(-126)=505=4
or: -126=41 => 4*1*41=164 => 1-4*1*(-126)=1-164=-163=4
or...
[SOLVED] Simple algebra problem (fields)
Homework Statement
Solve x²+x+41=0 in the fields Z43 and Z167
2. The attempt at a solution
Well Z43={0,1,...,42} so any y that is n=0 mod 43 works...
x²+x+41=0=43 -> x²+x=2 -> x=1
Is this how it's done or am I doing it incorrectly?
If the...
Ok, many thanks. Though I'm still not sure if I understand this. I mean it's quite unclear to me how these are used.
Edit: The problem is the following:
We have vectors a=(a1,a2,a3) and b=(b1,b2,b3)
Express the spin state |+>b as a linear combination of the normalized eigenvectors of the...
I have trouble understanding the concept of spin (spin 1/2 in this case). In Introduction to Quantum Mechanics Griffiths states that "the generic spinor X can be expressed as a linear combination of [eigenvectors of the spin component Sx]
\chi = \frac{a+b}{\sqrt{2}}\chi^{(x)}_+ +...
Homework Statement
Let G be a group and let #G=77. Prove the following:
a) G is cyclic, if there is such an element a in G that a21≠1 and a22≠1
b) If there are such elements a and b, so that ord(a)=7 and ord(b)=11, then G=<a,b>
2. Homework Equations , 3. The Attempt at a Solution
I...
Yes, of course. Whenever an object is at some explicit position, it is always at some explicit moment of time, too, even though their relation wouldn't be explicitly defined. Classically, at least. And when and object moves, time flows also. There is no change of position if there is no passing...
Well the book says... "If the force is independent of -- time, then..."
Possibly. I don't have the time to think about it thoroughly right now, but I'll ponder it later and report back.
Yes, I know. But if a function is not dependend on a variable, then shouldn't derivating the function with respect to that variable return zero? If f(x)=ax and neither a nor x is dependend on y, then df/dy=0?
Edit: Well you posted that latter post and for some reason I didn't see it though I...
[SOLVED] A very simple question about velocity and acceleration
Homework Statement
I should be way over this by now (I took elementary mechanics a year ago), but occasionally I find out there's unacceptably much I don't understand about very elementary physics (perhaps is it a sign to be...
\int e^{-\xi x^2}=\frac{\sqrt{\pi}\ erf(\sqrt{\xi}x)}{2\sqrt{\xi}}\ \ \ ?
I've never encountered an error function before in any homework problem, so I automatically assumed that I had done something wrong.
[SOLVED] Perturbation of the simple harmonic oscillator
Homework Statement
An additional term V0e-ax2 is added to the potential of the simple harmonic oscillator (V and a are constants, V is small, a>0). Calculate the first-order correction of the ground state. How does the correction change...