Firstly, I had forgotten to include the final sentence in Born's quote:
"... In this sense the law of causation is therefore empty; physics is in the nature of the case indeterminate, and therefore the affair of statistics."
Secondly, after providing the reader with the above quotes...
I see...
And I guess this is a direct result of the nature of the Schrodinger equation?
Also, is Born suggesting that "causality" breaks down (or, rather, that "causality is... empty") because the evolution of the probability function depends on this undefined quantity \Psi which (although...
(The following is a purely qualitative consideration of Quantum Mechanics)
In a particular Quantum Mechanics text, I've come across the following quote which I'm having some difficulties interpreting.
"We describe the instantaeous state of the system by a quantity \Psi , which satisfies a...
The nature of the infinite square well is such that there is always symmetry about the center (inside, the stationary states represent standing waves). In my particular case, I have chosen the center to lie at x=0 so that I may employ the odd-ness of the function f(x) = x and pursue the methods...
Homework Statement
A particle of mass m in the infinite square well of width a at time t = 0 is in a linear superposition of the ground- and the first excited- eigenstates, specifically it has the wave function
$$| \Psi(x,t) > = A[ | \psi_1 > + e^{i \phi} | \psi_2 >$$
Find the...
Thanks!
I'm not quite sure I can 'visualize' it too well, but-- in spite of this-- I think I understand it much better now.
The most important facet of this integral is the fact that it's, as you said, definite . This would force the x-variables to become constants after the integral is...
Homework Statement
This is a much more general question regarding differential equations; however, since it was presented in a quantum mechanics text (and physicists often make appeals to empirical considerations in their mathematics), I thought it might be appropriate to post here.
The...
Sure. The given guassian integrals are from 0 to inf., but the problem requires us to integrate from negative inf. to inf. (this is also why I said we would need to multiply by two).
Perhaps I should have simply listed the integrals from negative inf. to inf. in the outset, so that they...
Homework Statement
Consider the gaussian distribution
ρ(x) = Aexp[(-λ^2)(x-a)^2] ,
where A, a, and λ are positive real constants.
(a) Find A such that the gaussian distribution function is normalized to 1.
(b) Find <x> (average; expected value) , <x^2>, and σ (standard deviation).
(c)...
Ahh, I see.
Though, I'm still having some trouble understanding why the H-field doesn't equal 0 in this case.
From Maxwell's equation, we can invoke Stoke's Theorem to obtain the following relation:
\intH \bullet dl = I(free)
Moreover, Hemholtz' theorem guarantees a viable solution from the...
I've personally never heard of this relation, but another method (I think) might help cast some light on the situation is through the direct calculation of the induced bound currents:
Jb = \nabla χ M
and
Kb = M χ \hat{n}
where Jb is the induced volume current density (I/A), and Kb...
Ah, I see what you're saying.
There are two ways to go about solving for the B-field here:
1) Ampere's Law, which corresponds to part a:
\ointB \bullet dl = \muI(enc)
2) Invoking the H-field, which corresponds to part b:
\ointH \bullet dl = I(free)
and
H = \frac{1}{\mu}B - M...
Symmetry, here, is merited through the definition of H:
H = \frac{1}{\mu}B - M
Since both M and B point in the z-direction (M is given; B is always points in the z-direction inside a solenoid), H must also point in the z-direction.
Hope this helped. :3
A "magnetic dipole" is, as described above, a vague and ambiguous term. Indeed, magnetic dipoles do not even exist in nature (div(B) = 0, always). In a general sense, though, all magnetic field lines are not always normal to the current-carrying surface.
This follows directly from the...