# 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. ### 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##.
4. ### 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}}
5. ### 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}##.
6. ### 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)##
7. ### Infinite potential well

I understand that. But could you give me example of some specific situation.
8. ### 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##?
9. ### 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?
10. ### 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...
11. ### 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^*)
12. ### 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^*)
13. ### Infinite potential well

I didn't get the answer that I'm looking. My questions: Did wave function describes motion of particle? What kind of particle mass are good enough to be treated in this model? And And also why we don't draw ##\phi_{-n}(x)##?
14. ### Quantum mechanics probability

In the one moment you accept something in the other you're not sure why? Why probability density in quantum mechanics is defined as ##|\psi|^2## and no just ##|\psi|## if we know that ##|\psi|## is also positive quantity.
15. ### Infinite potential well

In one dimensional problem of infinite square potential well wave function is ##\phi_n(x)=\sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L}## and energy is ##E_n=\frac{n^2\pi^2\hbar^2}{2mL^2}##. Questions: What condition implies that motion is one dimensional. Did wave function describes motion of...
16. ### Angle between spins

Ok if I don't know that. I have some up spin. How to get up spin which is rotate for angle ##\theta## from that spin. Can I use Pauli matrices and spherical coordinates and get that result?
17. ### Angle between spins

But why you get ##\frac{\theta}{2}## in matrix if you rotate for angle ##\theta##?
18. ### Angle between spins

If ##|\alpha>## is spin up, and ##|\beta>## is spin down. Then if angle between those spins and some other up and down spin is ##\theta##, then |\alpha'>=\cos \frac{\theta}{2}|\alpha>+\sin \frac{\theta}{2}|\beta> |\beta'>=\sin \frac{\theta}{2}|\alpha>-\cos \frac{\theta}{2}|\beta> Why?
19. ### Heisenberg hamiltonian

Why is minus sine in definition of hamiltonian H=-\sum_{i,j}J_{i,j}(S_{i}^+S_{j}^-+S_i^zS_j^z) Why not? H=\sum_{i,j}J_{i,j}(S_{i}^+S_{j}^-+S_i^zS_j^z)
20. ### Statistical operator

Of course. My example wasn't so good. Suppose I have matrix \hat{\rho} = \begin{bmatrix} \frac{1}{3} & 5 & 6 \\[0.3em] 5 & \frac{1}{3} & 6 \\[0.3em] 5 & 6 & \frac{1}{3} \end{bmatrix} Why now \hat{\rho} always commute with Hamiltonian?
21. ### Statistical operator

\hat{\rho} = \begin{bmatrix} \frac{1}{3} & 0 & 0 \\[0.3em] 0 & \frac{1}{3} & 0 \\[0.3em] 0 & 0 & \frac{1}{3} \end{bmatrix} If I have this statistical operator I get i\hbar\frac{d\hat{\rho}}{dt}=0 So this is integral of motion and...