Recent content by matematikuvol

Interesting. Why 3 fermions? Why not 3 bosons? Or perhaps 2 fermions or to bosons?

What is quantisation axis? In many books authors just say that we choose that z is quantization axis.

##[H,x^2]=[\frac{p^2}{2m},x^2]=\frac{1}{2m}[p^2,x^2]=p[p,x^2]+[p,x^2]p## ##[p,x^2]=-2i\hbar x## from that ##[H,x^2]=-2i\hbar px-2i\hbar xp## from that ##[H,[H,x^2]]=p[\frac{p^2}{2m},-2i\hbar x]+[\frac{p^2}{2m},-2i\hbar x]p+p[\frac{1}{2}m\omega^2x^2,-2i\hbar x]+[\frac{1}{2}m\omega^2x^2,-2i\hbar...

In Dirac definition ##\delta(x)## is ##\infty## when ##x=0##, and ##0## when ##x\neq 0##. My question is when I have some ##\alpha \delta(x)## could I interpretate this like function which have value ##\alpha## in point ##x=0##?

For example you have spin ##S=\frac{7}{2}## and for example ##J=10## quantum Heisenberg model. And you have Monte Carlo simulation code for classical Heisenberg ##S=\infty##. What should you use for ##J## in classical Heisenberg model Monte Carlo code?

One example will be enough...

I'm speaking in general. I just see that in some papers some authors uses for example four sublattices for body centered cubic lattice. Why not two? I don't understand this.

In ordinary definition antiferromagnet lattice has to sublattices, one with spins up, and one with of spin down in ##T=0##. Why in some cases people discuss situations with four or even more subblatices? Do you have explanation for this? Some references maybe?

In quantum Heisenberg model \hat{H}=-J\sum_{\vec{n},\vec{m}}\hat{\vec{S}}_{\vec{n}}\cdot \hat{\vec{S}}_{\vec{m}} ##J## can be obtained from dispersion experiment. For large spin ##S## even classical Heisenberg model is good for description of Curie temperature for example. Is that with the same...

Suppose that problem is MC simulation of 2d Ising model with ##L^2## lattice sites. What is the one time step of that simulation?

What is referred as one Monte Carlo step. In all books, papers people is written that was performed ##5 \cdot 10^{6}## MCS on all system sizes. Or the time is measured in MCS. But what is referred as one MCS? For example in MC simulation of Ising model what is a one MCS?

Thanks for you're answer. I suppose like ##df(x,y)=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy## special case ##\frac{df}{dx}dx=df(x)##

I made a mistake. But I'm asking when you get that ##(\frac{d^n}{dx^n})_{x_0}##? Please answer my question if you know. In e^{\alpha\frac{d}{dx}}=1+\alpha\frac{d}{dx}+\frac{\alpha^2}{2!}\frac{d^2}{dx^2}+... you never have ##x_0##.

Ok but that is equal to \sum^{\infty}_{n=0}\frac{\alpha^n}{n!}(\frac{df}{dx})_{x_0} and how to expand now e^{\alpha\frac{d}{dx}}

I have a problem with that. So f(x+\alpha)=f(x)+\alpha f'(x)+... My problem is that we have ##\frac{df}{dx}## and that isn't value in some fixed point ##x##. This is the value in some fixed point ##(\frac{df}{dx})_{x_0}##.