Recent content by pines-demon

If you start with an eigenstate of ##H##, ##H|\phi_i\rangle=E_i|\phi_i\rangle## then you can show that the state evolves as $$|\psi(t)\rangle=e^{iE_i t/\hbar}|\phi_i\rangle$$ So now if you start with a sum of eigenstates ##\sum_j \alpha_j |\phi_j\rangle##, then $$|\psi(t)\rangle=\sum_j e^{iE_j...

Let us write $$|\uparrow\rangle=\begin{pmatrix}1\\0\end{pmatrix};|\downarrow\rangle=\begin{pmatrix}0\\1\end{pmatrix}$$ then your initial state is generally written as $$|\psi(0)\rangle=\begin{pmatrix}\alpha\\\beta\end{pmatrix}$$ thus you need to solve Schrödinger's equation $$i\hbar...

I was wondering where the ##4\pi## went and where the 2 came from. Using ##h## instead of ##\hbar## should be forbidden by now…

Obviously Ohm's law holds in metals, but any true justification has to come from a fully quantum-many-body theory when you show that you can neglect most (but not all of the interaction terms). The number of assumptions that a book takes in order to simplify it like that is not small.

Is that even true (putting aside that you cannot bring a mass to ##c##)? Edit: looking at the magnetic field of a moving charge, the magnetic field has a factor ##(1-v^2/c^2)## in the numerator, so it may go to zero when ##v\to c##. I would also like a confirmation that Maxwell came up with...

You all gotta love how PF can get hot on a simple question. We are already at three pages and still we do not know if OP is getting anything from what we already said because OP is not responding.

For entangled particles the state in the ##z##-axis is something like this $$|\Psi\rangle=\frac1{\sqrt2}(|\uparrow\downarrow\rangle-|\downarrow\uparrow\rangle)$$ It is not separable. Thus there is no ##\hat{\mathbf n}## and no single particle operator ##\mathbf S_{\hat{\mathbf n}}## that will...

Other observables have a clear picture. Positions relates to positions in space, momentum to momentum measurements and so on. The main distinction is that the Hilbert space for a single 1/2-spin particle is 2 dimensional. Please clarify, up to now we have not discussed EPR in any way, this is...

There is one way to carry out that measurement if you know how to prepare the state. You just run the preparation backwards (Hermitian conjugate of the gates you used to build the state). This is a common technique to check the fidelity of your state. Start from a given state (let's say...

Are you following a specific reference?

or about 1 foot/nanosecond (0.9836 ft/ns if you want to be exact). We can even go weirder, ##c=1.8026## terafurlong/fortnight in FFFF units.

Let us put younger/older versions aside (that requires relativity), as said above that would lead to relativistic mechanics or to quantum gravity. It is unclear many-worlds interpretation can explain either of those. MWI says that every measurement that breaks a quantum superposition would lead...

Earlier anecdote missed this story of Einstein and the Planck Medal (I did not include it because it was not about the Nobel Prize): Photo: from Wikipedia Max Planck Medal.

Yes, for an ensemble of spins aligned along ##\hat{\mathbf n}##, the measurement of ##\mathbf S_{\hat{\mathbf n}}## is always ##+\tfrac12## (earlier I used ##\hbar=1## but if you include it, you get ##+\hbar/2##).

Usually physics is very bad at answering "why" questions. As others have suggested you can derive it from a couple of principles, but then you can ask "why" we have those principles. In the end ##c## turns out to be what it is because it confirms what we measure. Try to reformulate your...