Homework Statement
##p_k## refers to prime numbers ##p_1<\cdots<p_k<\cdots ##
I thought that it could have something to do with the FTA so all natural numbers are composed of a unique product of primes.
So I need to show ## \text{P} ( X=M p_l \cap X = N p_m ) = \text{P} ( X=M p_l )...
I think my questions should be:
How does isospin, I, affect the symmetry of the ## \Psi_{\text{flavor}} ## wavefunction?
Spins of like quarks have to be in the S=1 state by symmetry, and for J=3/2 the spins have to be parallel. Doesn't a mix of anti-symmetric states in the spin and flavor...
Yes that was what I was attempting to get at, the color wavefunction is antisymmetric, assuming we are in l=0 we have the space wavefunction symmetric and now I am looking at the product of the spin and flavor which I require to be together symmetric and to see how many particles there are, but...
yes I forgot and the other, symm. ## \frac{1}{\sqrt{2}} \left( | \uparrow \downarrow \rangle + | \downarrow \uparrow \rangle \right) ## ...
I don't really know how to ask this question very well, but, it is how spin and color wave-functions are related to whether or not it is symmetric or not...
If you have a meson in the states
## ^3S_1## and ## ^1S_0 ## this means that ##J^P = 1^+ ## and ## 0^+## doesn't it?
But if you have excited states
## ^1P_1 ## this is ##J^P=1^- ## but isn't ## ^3P_1 ## supposed to be ##J^P = 1^- ##? Does this matter?
##^3P_0##, ##^3P_1## and ##^3P_2## for...
OK, so would a way to look at that operation be:
##I_- |\pi N; \frac{3}{2},\frac{3}{2}\rangle = I_- |\pi ;1,1\rangle \otimes | N; \frac{1}{2},\frac{1}{2}\rangle + |\pi ;1,1\rangle \otimes I_-| N; \frac{1}{2},\frac{1}{2}\rangle## ?
Which will give me
## k_1 |\pi^0 p \rangle + k_2 |...
Notation confusion; ## |\pi N; I, I_3 \rangle ## states
In my book it says for the ##\pi N ## state:
##|\pi N; \frac{3}{2},\frac{3}{2}\rangle =|\pi ;1,1\rangle | N; \frac{1}{2},\frac{1}{2}\rangle##
firstly, does this mean:
##|\pi N; \frac{3}{2},\frac{3}{2}\rangle =|\pi ;1,1\rangle...
You have managed to extrapolate an awful lot from the three word post. Obviously it was a bad bump.. I'm sure the members will survive. I just wanted a reason for no reply after 100+ views (i.e. unclear etc.)
I have one now. There was no urgency. This used to be a place where I could discuss...
It's very common now that I post something, attempting to be as clear as possible, 100s look at the thread but no-one replies. It didn't used to be like that.
I'm looking at scattering theory and eventually the Born approximation... In the notes I am reading it says we want to solve the Schrodinger equation written in the form:
##\left(\nabla ^2+k^2\right)\psi =V \psi##
Of which there are two solutions, the homogeneous solution which tends to...
##F(Y(t))-F(Y(0)) = \sin(Y(t)) - \sin(Y(0)) ## this is the relationship between the RHS and the Ito formula which is given in terms of ## F(b,Y(b) - F(a, T(a)) ## it should read
## F(t, Y(t))-F(0, Y(0)) = \sin(Y(t)) - \sin(Y(0)) ##
I am to use the Ito formula to get an expression for the...
I have a question about the functions g and h in the Ito formula (below). The question is about finding
##F(Y(t))-F(Y(0)) = \sin(Y(t)) - \sin(Y(0))##
given that
## Y(t) - Y(0) = \int_0^t dW(t)##
Ito's formula:
##F(b,Y(b)) - F(b,Y(b)) = \int_a^b \frac{\partial F}{\partial...