Homework Statement
i'm trying to calculate the charge operator for a complex scalar field. I've got the overal problem right but I'm confused about this:
On page 18 of Peskin, it is written that the conserved current of a complex scalar field, associated with the transformation ##\phi...
Homework Statement
Discuss the continuity, derivability and differentiability of the function
f(x,y) = \frac{x^3}{x^2+y^2} if (x,y)≠(0,0) and 0 otherwise
Homework Equations
if f is differentiable then ∇f.v=\frac{∂f}{∂v}
if f has both continuous partial derivative in a neighbourhood of x_0...
I'll look at the action of the operator on a general eigenstate
Sin\phi \left| n \right\rangle
in the \phi basis
\frac{e^{i\phi}-e^{-i\phi}}{2i} e^{in\phi} = \frac{e^{i(n+1)\phi}-e^{i(n-1)\phi}}{2i}
Sin\phi \left| n \right\rangle...
The ϕ operator in the ϕ becomes the identity operator.
With this in mind, i write Sin\phi = \frac{e^{i\phi}-e^{-i\phi}}{2i}
i'm not really sure where to go from here.
What is e^{i\phi}\left|1\right\rangle ?
Homework Statement
Consider a particle on a ring with radius R in a plane.
The Hamiltonian is H_0 = -\frac{\hbar^2}{2mR^2}\frac{d^2}{d\phi^2}
The wavefunction at t=0 is \psi=ASin\phi
Find the mean value of the observable Sin\phi
Homework Equations
The eigenfunction are
\psi_n =...
I don't think you can do that as the higher hermite polinomials are not zero.
I've figured the first and second integrals and they are
c_0 = \frac{1}{\sqrt{e}^{4}}
c_1 =0
c_0 differs from your method.
i still need to find the last integral though.
[/itex]Homework Statement
Find the first three coeficents c_n of the expansion of Cos(x) in Hermite Polynomials.
The first three Hermite Polinomials are:
H_0(x) = 1
H_1(x) = 2x
H_0(x) = 4x^2-2The Attempt at a Solution
I know how to solve a similar problem where the function is a polynomial of...
You can use this little theorem that is very useful in situatons like this one.
Call your sequence a_n
If a_n > 0
you calculate this limit lim {a_{n+1} \over a_n}
if that limit is beetween 0 and 1, but not 1,then a_n{\rightarrow} 0
if that limit is greater than 1 then...
In your first question you show that your sequence lies beetween two sequence that both goes to zero 0≤An≤0 this implies An → 0
It's important that you show that it lies BEETWEEN two sequences.
In your secondo question you show that your question is less than infinity, that does not make it go...