# Search results

1. ### Phonons: For oscillator wave function

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

What is quantisation axis? In many books authors just say that we choose that z is quantization axis.
3. ### Harmonic oscilator Tamvakis

##[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...
4. ### Delta function

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##?
5. ### Classical and quantum Heisenberg model

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?
6. ### Antiferromagnet more subblatices

One example will be enough...
7. ### Antiferromagnet more subblatices

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.
8. ### Antiferromagnet more subblatices

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?
9. ### Classical and quantum Heisenberg model

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...
10. ### Monte Carlo step

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

What is refered 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 refered as one MCS? For example in MC simulation of Ising model what is a one MCS?
12. ### Derivative question

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)##
13. ### Translation operator

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##.
14. ### Translation operator

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}}
15. ### Translation operator

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}##.
16. ### Derivative question

Is then in eq ##y'(x)=y(x)##, ##y(x)## value of function or function? :D Question for WannabeNewton. micromass ok called whatever you want. Why isn't equal ##df=\frac{df}{dx}##?
17. ### Derivative question

I didn't asked that. I asked why we can multiply and devide with ##dx##.
18. ### Translation operator

e^{\alpha\frac{d}{dx}}=1+\alpha\frac{d}{dx}+\frac{\alpha^2}{2!}\frac{d^2}{dx^2}+...=\sum^{\infty}_{n=0}\frac{\alpha^n}{n!}\frac{d^n}{dx^n} Why this is translational operator? ##e^{\alpha\frac{d}{dx}}f(x)=f(x+\alpha)##
19. ### Derivative question

If ##f=f(x)## why then is ##df=\frac{df}{dx}dx##?
20. ### Linear operator

Sorry but I think that you didn't read my post. I defined multiplication operator which goes from ##f## to ##5f##.
21. ### Linear operator

I define A as multiplicative operator clearly.
22. ### Linear operator

Linear operator A is defined as A(C_1f(x)+C_2g(x))=C_1Af(x)+C_2Ag(x) Question. Is A=5 a linear operator? I know that this is just number but it satisfy relation 5(C_1f(x)+C_2g(x))=C_15f(x)+C_25g(x) but it is also scalar. Is function ##A=x## linear operator? It also satisfy...
23. ### Infinite potential well

I understand that. But could you give me example of some specific situation.
24. ### Divergence question

Yes. But I'm not sure why is that correct? Could you explain me that?
25. ### Divergence question

I see identity in one mathematical book div \vec{A}(r)=\frac{\partial \vec{A}}{\partial r} \cdot grad r How? From which equation?
26. ### Infinite potential well

Ok but from ##C_1^2+C_2^2=1## and some other physical behavior could I say something about ##C_1^2## and ##C_2^2##?
27. ### Infinite potential well

Well from \int^{a}_0 (C_1\sin \frac {\pi x}{a}+C_2 \sin \frac{2\pi x}{a})^2=1 I get ##C_1^2+C_2^2=\frac{2}{a}## what next?
28. ### Infinite potential well

One more question. By solving Sroedinger eq we get ##\varphi_n(x)=\sqrt{\frac{2}{a}}\sin \frac{n\pi x}{a}## ##E_n=\frac{n^2\pi^2\hbar^2}{2ma^2}## But for example solution of Sroedinger eq is also ##C_1sin\frac {\pi x}{a}+C_2\sin\frac{2\pi x}{a}## in which state is particle? What is the energy...
29. ### Quantum mechanics probability

Well I agree with second reason. But you can normalized state in such way that \int^{\infty}_{-\infty}|\psi(x,t)|dx=1 Right? And the second one. Why current is defined like \vec{j}=\frac{\hbar}{2im}(\psi^*\frac{d}{dx}\psi-\psi\frac{d}{dx}\psi^*)
30. ### Quantum mechanics probability

I believed that theory is consistent. But why Bohm took ##|\psi(x,t)|^2##? Is there some bond with \vec{j}=\frac{\hbar}{2im}(\psi^*\frac{d}{dx}\psi-\psi\frac{d}{dx}\psi^*)