Thanks for answering, but how would it be in terms of derivatives? Normally It would be:
f=\sum_{m,n} \frac{a^m a^{\dagger m}}{n!m!}\frac{\partial^{n+m} f}{\partial a^n \partial a^{\dagger m}}
But in this case I guess I have to take into account that they're noncommuting.
Homework Statement
Need to show that [a,f(a,a^\dagger]=\frac{\partial f}{\partial a^\dagger}
Homework Equations
[a,a^\dagger]=1
The Attempt at a Solution
Need to expand f(a,a^\dagger) in a formal power series. However I don´t know how to do it if the variables don´t commute.
Homework Statement
I have to prove the Fierz rearrengement identity for Weyl Fermions. Eq 2.20 in Martin's supersymmetry primer:
\chi_\alpha(\xi\eta)=-\xi_\alpha(\eta\chi)-\eta_\alpha(\chi\xi)
Homework Equations
We have that the antisimetric tensor raises and lowers indices.
The Attempt at...
Homework Statement
I need to find the green function for a dielectric sphere (\epsilon_1) inside another dielectric medium (\epsilon_2) using the method of images.
Homework Equations
In gaussian units I have: \phi=\frac{q}{\epsilon|r-r1|}
The Attempt at a Solution
Due to the symmetry of the...
Thanks a lot for answering.
I've done that but I'm still stuck. I forgot to mention this was for bosons so the commutation relation must hold [a,a^\dagger]=1. From it I got:
a(a^\dagger)^n=n(a^\dagger)^{n-1}+(a^\dagger)^n a
I suppose the relation holds for \langle m | n \rangle and I must...
Hello,
I'm currently studying second quantization. I need to prove <n^\prime| n>=\delta_{n^\prime n} by mathematical induction in the number of particles representation. However I don't know how to do this proof having two natural numbers n and n^\prime. Must I prove it holds for <0|0>, <0|1>...
Homework Statement
There is a charged particle (charge=q) moving on the x-axis such that x(t)=A\,sin(\omega t). Prove that:
\int <\rho>\,dV=q Homework Equations
We have the following equations:
<\rho>=\frac{1}{T} \int_0^T \rho\, dt
Where T=\frac{2 \pi}{\omega}
The Attempt at a Solution
So...
Hello, the question does say "Dissipative Potential". From what I've seen in class, if the force can be derived from a potential, the normal Euler-Lagrange equations are still valid. Therefore I used the following:
\mathcal{L}=\frac{1}{2}(m-k)\dot{y}^{2}-mgy
Euler-Lagrange...
Hello, First post hear so bear with me.
I have a mass in free fall with a viscous friction which can be derived from the dissipative potential Kv2/2. I must find the Lagrangian and proove that the maximum speed is v=mg/K. I have the following Lagrangian...